## Ward, Michael J.

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 Author ID: ward.michael-j Published as: Ward, Michael J.; Ward, M. J.; Ward, Michael more...less Homepage: https://personal.math.ubc.ca/~ward/ External Links: MGP
 Documents Indexed: 156 Publications since 1989 4 Contributions as Editor Co-Authors: 88 Co-Authors with 135 Joint Publications 2,427 Co-Co-Authors
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### Co-Authors

 15 single-authored 26 Wei, Juncheng 22 Kolokolnikov, Theodore 9 Reyna, Luis Guillermo M. 9 Tzou, Justin C. 8 Iron, David 7 Iyaniwura, Sarafa A. 6 Lindsay, Alan E. 5 Gou, Jia 5 Keller, Joseph Bishop 5 Titcombe, Michèle S. 4 King, John Robert 4 Kropinski, Mary Catherine A. 4 Nec, Yana 4 Odeh, F. M. 4 Paquin-Lefebvre, Frédéric 4 Straube, Ronny 4 Sun, Xiaodi 3 Breña-Medina, Víctor F. 3 Cheviakov, Alexei F. 3 Coombs, Daniel 3 Howison, Samuel Dexter 3 Nagata, Wayne 3 Sun, Wentao 3 Tse, Wang Hung 2 Avitabile, Daniele 2 Burger, Martin 2 Champneys, Alan R. 2 Chen, Wan 2 Edelstein-Keshet, Leah 2 Fadai, Nabil T. 2 Gomez, Daniel 2 Lacey, Andrew A. 2 Li, Yuexian 2 Macdonald, Colin B. 2 Moyles, Iain R. 2 O’Malley, Robert E. jun. 2 Rumsey, John R. 2 Small, Tim 2 Stafford, Douglas 2 Trinh, Philippe H. 2 Van de Velde, Eric F. 2 Zmurchok, Cole 1 Audsley, Neil C. 1 Bernoff, Andrew J. 1 Bertozzi, Andrea Louise 1 Bluman, George W. 1 Brădean, Radu 1 Brauer, Fred 1 Bressloff, Paul C. 1 Brewster, M. Q. 1 Bridge, Lloyd J. 1 Broadbridge, Philip 1 Chang, Yifan 1 Chiang, Wei-Yin 1 Cohen, Donald Sussman 1 Costello, Christopher J. 1 David, Jummy Funke 1 Delgado, M. I. 1 Earnshaw, Berton A. 1 Falcke, Martin 1 Gavaghan, David J. 1 Grierson, C. 1 Guo, Yujin 1 Henshaw, William D. 1 Hormozi, Sarah 1 Houston, Paul 1 Jamieson-Lane, Alastair 1 Johnson, Shane D. 1 Kang, Kyungkeun 1 Kurella, Venu 1 Laforgue, Jacques G. L. 1 Lai, Pik-Yin 1 Lee, June-Yub 1 Maini, Philip Kumar 1 McInerney, Darragh 1 Ou, Chunhua 1 Pan, Zhenguo 1 Peirce, Anthony P. 1 Randrianandrasana, Michel F. 1 Ridgway, Wesley 1 Rottschäfer, Vivi 1 Rozada, Ignacio 1 Russell, Robert D. 1 Ruuth, Steven J. 1 Sleeman, Brian David 1 Son, Steven Forrest 1 Tang, Tao 1 Wei, Xueyong 1 Wetton, Brian R. 1 Wetton, Brian T. R. 1 Wolf, Sven Andreas 1 Xie, Shuangquan
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### Serials

 24 SIAM Journal on Applied Mathematics 22 European Journal of Applied Mathematics 17 Studies in Applied Mathematics 14 SIAM Journal on Applied Dynamical Systems 8 Physica D 5 IMA Journal of Applied Mathematics 5 Journal of Engineering Mathematics 5 Methods and Applications of Analysis 5 Multiscale Modeling & Simulation 4 Bulletin of Mathematical Biology 4 Journal of Nonlinear Science 4 Discrete and Continuous Dynamical Systems. Series B 3 Nonlinearity 3 Applied Mathematics Letters 2 Journal of Environmental Economics and Management 2 Interfaces and Free Boundaries 2 Mathematical Modelling of Natural Phenomena 1 Communications on Pure and Applied Mathematics 1 International Journal of Mechanical Sciences 1 Journal of Mathematical Biology 1 Journal of Statistical Physics 1 Canadian Mathematical Bulletin 1 International Journal for Numerical Methods in Engineering 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 Numerical Functional Analysis and Optimization 1 Applied Numerical Mathematics 1 Mathematical and Computer Modelling 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Review 1 The Canadian Applied Mathematics Quarterly 1 Mathematical Problems in Engineering 1 Natural Resource Modeling 1 Combustion Theory and Modelling 1 The ANZIAM Journal 1 Analysis and Applications (Singapore) 1 Mathematical Biosciences and Engineering 1 Discrete and Continuous Dynamical Systems. Series S 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
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### Fields

 133 Partial differential equations (35-XX) 40 Biology and other natural sciences (92-XX) 23 Numerical analysis (65-XX) 15 Fluid mechanics (76-XX) 13 Ordinary differential equations (34-XX) 10 Dynamical systems and ergodic theory (37-XX) 9 Mechanics of deformable solids (74-XX) 9 Classical thermodynamics, heat transfer (80-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 3 Probability theory and stochastic processes (60-XX) 3 Mechanics of particles and systems (70-XX) 3 Optics, electromagnetic theory (78-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX)

### Citations contained in zbMATH Open

133 Publications have been cited 1,750 times in 737 Documents Cited by Year
The stability of spike solutions to the one-dimensional Gierer-Meinhardt model. Zbl 0983.35020
Iron, David; Ward, Michael J.; Wei, Juncheng
2001
Touchdown and pull-in voltage behavior of a MEMS device with varying dielectric properties. Zbl 1103.35042
Guo, Yujin; Pan, Zhenguo; Ward, M. J.
2005
Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model. Zbl 1030.35011
Ward, M. J.; Wei, J.
2003
Strong localized perturbations of eigenvalue problems. Zbl 0778.35081
Ward, Michael J.; Keller, Joseph B.
1993
Summing logarithmic expansions for singularly perturbed eigenvalue problems. Zbl 0778.35082
Ward, Michael J.; Henshaw, William D.; Keller, Joseph B.
1993
The existence and stability of asymmetric spike patterns for the Schnakenberg model. Zbl 1152.35397
Ward, Michael J.; Wei, Juncheng
2002
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime. Zbl 1136.35003
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
An asymptotic analysis of the mean first passage time for narrow escape problems. I: Two-dimensional domains. Zbl 1203.35023
Pillay, S.; Ward, M. J.; Peirce, A.; Kolokolnikov, T.
2010
Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain. Zbl 1178.35039
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2009
The stability and dynamics of localized spot patterns in the two-dimensional Gray-Scott model. Zbl 1223.35033
Chen, W.; Ward, M. J.
2011
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: The low feed-rate regime. Zbl 1145.65328
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
The dynamics of multispike solutions to the one-dimensional Gierer-Meinhardt model. Zbl 1019.35016
Iron, David; Ward, Michael J.
2002
An asymptotic analysis of the mean first passage time for narrow escape problems. II: The sphere. Zbl 1204.35030
Cheviakov, Alexei F.; Ward, Michael J.; Straube, Ronny
2010
Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps. Zbl 1090.35070
Kolokolnikov, T.; Titcombe, M. S.; Ward, M. J.
2005
Asymmetric spike patterns for the one-dimensional Gierer-Meinhardt model: Equilibria and stability. Zbl 1010.35002
Ward, M. J.; Wei, J.
2002
On the exponentially slow motion of a viscous shock. Zbl 0824.76042
Reyna, Luis G.; Ward, Michael J.
1995
Hopf bifurction of spike solutions for the shadow Gierer-Meinhardt model. Zbl 1063.35030
Ward, M. J.; Wei, J.
2003
The existence and stability of spike patterns in a chemotaxis model. Zbl 1073.35118
Sleeman, B. D.; Ward, Michael J.; Wei, J. C.
2005
The slow dynamics of two-spike solutions for the Gray-Scott and Gierer-Meinhardt systems: competition and oscillatory instabilities. Zbl 1145.35404
Sun, Wentao; Ward, Michael J.; Russell, Robert
2005
Metastable bubble solutions for the Allen-Cahn equation with mass conservation. Zbl 0870.35011
Ward, Michael J.
1996
The stability of a stripe for the Gierer-Meinhardt model and the effect of saturation. Zbl 1210.35016
Kolokolnikov, Theodore; Sun, Wentao; Ward, Michael; Wei, Juncheng
2006
Diffusion on a sphere with localized traps: mean first passage time, eigenvalue asymptotics, and Fekete points. Zbl 1191.35032
Coombs, Daniel; Straube, Ronny; Ward, Michael
2009
The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime. Zbl 1304.35051
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2014
Optimizing the principal eigenvalue of the Laplacian in a sphere with interior traps. Zbl 1219.35155
Cheviakov, A. F.; Ward, M. J.
2011
The stability of localized spot patterns for the Brusselator on the sphere. Zbl 1302.35033
Rozada, Ignacio; Ruuth, Steven J.; Ward, M. J.
2014
First passage statistics for the capture of a Brownian particle by a structured spherical target with multiple surface traps. Zbl 1372.35021
Lindsay, Alan E.; Bernoff, Andrew J.; Ward, Michael J.
2017
A metastable spike solution for a nonlocal reaction-diffusion model. Zbl 0956.35011
Iron, David; Ward, Michael J.
2000
Oscillatory instabilities and dynamics of multi-spike patterns for the one-dimensional Gray-Scott model. Zbl 1197.35021
Chen, Wan; Ward, Michael J.
2009
Slowly varying control parameters, delayed bifurcations, and the stability of spikes in reaction-diffusion systems. Zbl 1364.35151
Tzou, J. C.; Ward, M. J.; Kolokolnikov, T.
2015
Asymptotic analysis of first passage time problems inspired by ecology. Zbl 1319.35275
Kurella, Venu; Tzou, Justin; Coombs, Daniel; Ward, Michael
2015
Asymptotics of some nonlinear eigenvalue problems for a MEMS capacitor: Part I: Fold point asymptotics. Zbl 1173.35625
Lindsay, A. E.; Ward, M. J.
2008
Dynamics and coarsening of interfaces for the viscous Cahn-Hilliard equation in one spatial dimension. Zbl 1136.74366
Sun, Xiaodi; Ward, Michael J.
2000
Reduced wave Green’s functions and their effect on the dynamics of a spike for the Gierer-Meinhardt model. Zbl 1063.35024
Kolokolnikov, Theodore; Ward, Michael J.
2003
An asymptotic analysis of a 2-D model of dynamically active compartments coupled by bulk diffusion. Zbl 1439.92024
Gou, J.; Ward, M. J.
2016
The dynamics of localized spot patterns for reaction-diffusion systems on the sphere. Zbl 1338.35248
Trinh, Philippe H.; Ward, Michael J.
2016
Hotspot formation and dynamics for a continuum model of urban crime. Zbl 1408.91169
Tse, W. H.; Ward, M. J.
2016
Eliminating indeterminacy in singularly perturbed boundary value problems with translation invariant potentials. Zbl 0767.65068
Ward, Michael J.
1992
The stability and dynamics of a spike in the 1D Keller-Segel model. Zbl 1133.35058
Kang, K.; Kolokolnikov, T.; Ward, M. J.
2007
The dynamics and pinning of a spike for a reaction-diffusion system. Zbl 1032.35029
Ward, Michael J.; McInerney, Darragh; Houston, Paul; Gavaghan, David; Maini, Philip
2002
Metastability for a generalized Burgers equation with applications to propagating flame fronts. Zbl 0919.35122
Sun, X.; Ward, M. J.
1999
Asymptotics beyond all orders for a low Reynolds number flow. Zbl 0880.76022
Keller, Joseph B.; Ward, Michael J.
1996
Asymptotics of some nonlinear eigenvalue problems modelling a MEMS capacitor. II: Multiple solutions and singular asymptotics. Zbl 1220.35108
Lindsay, A. E.; Ward, M. J.
2011
An asymptotic analysis of localized solutions for some reaction-diffusion model in multidimensional domains. Zbl 0932.35059
Ward, Michael J.
1996
Spots, traps, and patches: asymptotic analysis of localized solutions to some linear and nonlinear diffusive systems. Zbl 1393.35106
Ward, M. J.
2018
An explicitly solvable nonlocal eigenvalue problem and the stability of a spike for a sub-diffusive reaction-diffusion system. Zbl 1275.35020
Nec, Y.; Ward, M. J.
2013
The linear stability of symmetric spike patterns for a bulk-membrane coupled Gierer-Meinhardt model. Zbl 1419.35107
Gomez, Daniel; Ward, Michael J.; Wei, Juncheng
2019
Zigzag and breakup instabilities of stripes and rings in the two-dimensional Gray-Scott model. Zbl 1145.35388
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2006
The existence and stability of spike equilibria in the one-dimensional Gray – Scott model on a finite domain. Zbl 1125.35048
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
A hybrid asymptotic-numerical method for low Reynolds number flows past a cylindrical body. Zbl 0854.76028
Kropinski, M. C. A.; Ward, Michael J.; Keller, Joseph B.
1995
Metastable internal layer dynamics for the viscous Cahn-Hilliard equation. Zbl 0859.35008
Reyna, Luis G.; Ward, Michael J.
1995
Conditional mean first passage times to small traps in a 3-D domain with a sticky boundary: applications to T cell searching behavior in lymph nodes. Zbl 1339.92009
Delgado, M. I.; Ward, M. J.; Coombs, D.
2015
Oscillatory dynamics for a coupled membrane-bulk diffusion model with Fitzhugh-Nagumo membrane kinetics. Zbl 1347.35032
Gou, J.; Ward, M. J.
2016
The stability and slow dynamics of spot patterns in the 2D Brusselator model: the effect of open systems and heterogeneities. Zbl 1392.35039
Tzou, J. C.; Ward, M. J.
2018
Synchronized oscillatory dynamics for a 1-D model of membrane kinetics coupled by linear bulk diffusion. Zbl 1331.35038
Gou, J.; Li, Y. X.; Nagata, W.; Ward, M. J.
2015
Asymptotic methods for reaction-diffusion systems: past and present. Zbl 1334.92004
Ward, Michael J.
2006
The stability and slow dynamics of localized spot patterns for the 3-D Schnakenberg reaction-diffusion model. Zbl 1434.35019
Tzou, J. C.; Xie, S.; Kolokolnikov, T.; Ward, M. J.
2017
Metastable patterns, layer collapses, and coarsening for a one- dimensional Ginzburg-Landau equation. Zbl 0794.35119
Ward, Michael J.
1994
Dynamics and stability of spike-type solutions to a one dimensional Gierer-Meinhardt model with sub-diffusion. Zbl 1252.35033
Nec, Yana; Ward, Michael J.
2012
Explicitly solvable nonlocal eigenvalue problems and the stability of localized stripes in reaction-diffusion systems. Zbl 1338.35246
Moyles, I.; Tse, W. H.; Ward, M. J.
2016
Pattern formation and oscillatory dynamics in a two-dimensional coupled bulk-surface reaction-diffusion system. Zbl 1428.37071
Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J.
2019
Multiple steady-state solutions in a multijunction semiconductor device. Zbl 0739.34028
Ward, M. J.; Reyna, L. G.; Odeh, F. M.
1991
Numerical challenges for resolving spike dynamics for two one-dimensional reaction-diffusion systems. Zbl 1141.35389
Sun, Wentao; Tang, Tao; Ward, Michael J.; Wei, Juncheng
2003
Pulse-splitting for some reaction-diffusion systems in one-space dimension. Zbl 1145.35401
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
The stability of localized spikes for the 1-D Brusselator reaction-diffusion model. Zbl 1295.35038
Tzou, J. C.; Nec, Y.; Ward, M. J.
2013
Slow translational instabilities of spike patterns in the one-dimensional Gray-Scott model. Zbl 1105.35132
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2006
Logarithmic expansions and the stability of periodic patterns of localized spots for reaction-diffusion systems in $$\mathbb R^2$$. Zbl 1334.35347
Iron, David; Rumsey, John; Ward, Michael J.; Wei, Juncheng
2014
Asymptotic analysis of localized solutions to some linear and nonlinear biharmonic eigenvalue problems. Zbl 1219.35043
Kropinski, M. C.; Lindsay, A. E.; Ward, M. J.
2011
Spot dynamics in a reaction-diffusion model of plant root hair initiation. Zbl 1383.92048
Avitabile, Daniele; Breña-Medina, Victor F.; Ward, Michael J.
2018
A theory of synchrony by coupling through a diffusive chemical signal. Zbl 1376.92020
Gou, Jia; Chiang, Wei-Yin; Lai, Pik-Yin; Ward, Michael J.; Li, Yue-Xian
2017
Stripe to spot transition in a plant root hair initiation model. Zbl 06444870
Breña-Medina, V. F.; Avitabile, D.; Champneys, A. R.; Ward, M. J.
2015
Mathematical modeling of plant root hair initiation: dynamics of localized patches. Zbl 1302.35030
Breña-Medina, V.; Champneys, A. R.; Grierson, C.; Ward, M. J.
2014
Asymptotic methods for metal oxide semiconductor field effect transistor modeling. Zbl 0707.35130
Ward, M. J.; Odeh, F. M.; Cohen, D. S.
1990
Delayed reaction kinetics and the stability of spikes in the Gierer-Meinhardt model. Zbl 1368.35021
Fadai, Nabil T.; Ward, Michael J.; Wei, Juncheng
2017
Dynamic metastability and singular perturbations. Zbl 0910.35011
Ward, Michael J.
1998
An asymptotic study of oxygen transport from multiple capillaries to skeletal muscle tissue. Zbl 0990.92009
Titcombe, Michèle S.; Ward, Michael J.
2000
Internal layers, small eigenvalues, and the sensitivity of metastable motion. Zbl 0818.35008
Ward, Michael J.; Reyna, Luis G.
1995
Self-replication of mesa patterns in reaction-diffusion systems. Zbl 1136.35002
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2007
Bifurcation of spike equilibria in the near-shadow Gierer-Meinhardt model. Zbl 1063.35084
Kolokolnikov, Theodore; Ward, Michael J.
2004
Existence, stability, and dynamics of ring and near-ring solutions to the saturated Gierer-Meinhardt model in the semistrong regime. Zbl 1434.35017
Moyles, Iain R.; Ward, Michael J.
2017
Metastable dynamics and exponential asymptotics in multi-dimensional domains. Zbl 1007.35002
Ward, Michael J.
2001
Nonlinear dynamics of a periodically driven Duffing resonator coupled to a van der Pol oscillator. Zbl 1250.34032
Wei, X.; Randrianandrasana, M. F.; Ward, M.; Lowe, D.
2011
Reaction rate of small diffusing molecules on a cylindrical membrane. Zbl 1206.82150
Straube, Ronny; Ward, Michael J.; Falcke, Martin
2007
An asymptotic analysis of intracellular signaling gradients arising from multiple small compartments. Zbl 1182.92025
Straube, Ronny; Ward, Michael J.
2009
Asynchronous instabilities of crime hotspots for a 1-D reaction-diffusion model of urban crime with focused police patrol. Zbl 1397.35138
Tse, Wang Hung; Ward, Michael J.
2018
The stability and dynamics of hot-spot solutions to two one-dimensional microwave heating models. Zbl 1050.35008
Iron, David; Ward, Michael J.
2004
The dynamics of drops and attached interfaces for the constrained Allen-Cahn equation. Zbl 0988.76095
Stafford, D.; Ward, M. J.; Wetton, B.
2001
The stability and slow dynamics of two-spike patterns for a class of reaction-diffusion system. Zbl 1283.35113
Nec, Y.; Ward, M. J.
2013
Similarity: Generalizations, applications and open problems. Zbl 1188.00015
Bluman, G.; Broadbridge, P.; King, J. R.; Ward, M. J.
2010
Nonlinear eigenvalue problems under strong localized perturbations with applications to chemical reactors. Zbl 0728.65087
Ward, Michael J.; Keller, Joseph B.
1991
Transition to blow-up in a reaction-diffusion model with localized spike solutions. Zbl 1387.35338
Rottschäfer, V.; Tzou, J. C.; Ward, M. J.
2017
A novel approach to modelling the spatial spread of airborne diseases: an epidemic model with indirect transmission. Zbl 1467.92186
David, Jummy F.; Iyaniwura, Sarafa A.; Ward, Michael J.; Brauer, Fred
2020
Singular perturbations and a free boundary problem in the modeling of field-effect transitors. Zbl 0753.35112
Ward, Michael J.
1992
The onset of thermal runaway in partially insulated or cooled reactors. Zbl 0796.35060
Ward, Michael J.; Van de Velde, Eric F.
1992
On the asymptotic and numerical analyses of exponentially ill-conditioned singularly perturbed boundary value problems. Zbl 0824.65070
Lee, June-Yub; Ward, Michael J.
1995
Weakly nonlinear theory for oscillatory dynamics in a one-dimensional PDE-ODE model of membrane dynamics coupled by a bulk diffusion field. Zbl 1446.37071
Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J.
2020
The analysis of a two-phase zone with condensation in a porous medium. Zbl 1113.76458
Bridge, L.; Bradean, R.; Ward, M. J.; Wetton, B. R.
2003
Spike pinning for the Gierer-Meinhardt model. Zbl 0979.35142
Iron, David; Ward, Michael J.
2001
A practical method for finite element ring rolling simulation using the ALE flow formulation. Zbl 1125.74383
Davey, K.; Ward, M. J.
2002
Diffusion of protein receptors on a cylindrical dendritic membrane with partially absorbing traps. Zbl 1146.92005
Bressloff, Paul C.; Earnshaw, Berton A.; Ward, Michael J.
2008
Anomalous scaling of Hopf bifurcation thresholds for the stability of localized spot patterns for reaction-diffusion systems in two dimensions. Zbl 1391.35225
Tzou, J. C.; Ward, M. J.; Wei, J. C.
2018
Synchrony and oscillatory dynamics for a 2-d PDE-ODE model of diffusion-mediated communication between small signaling compartments. Zbl 1462.35227
Iyaniwura, Sarafa A.; Ward, Michael J.
2021
Competition instabilities of spike patterns for the 1D Gierer-Meinhardt and Schnakenberg models are subcritical. Zbl 1456.35013
Kolokolnikov, Theodore; Paquin-Lefebvre, Frédéric; Ward, Michael J.
2021
An asymptotic analysis of localized three-dimensional spot patterns for the Gierer-Meinhardt model: existence, linear stability, and slow dynamics. Zbl 1462.35031
Gomez, Daniel; Ward, Michael J.; Wei, Juncheng
2021
Spot patterns in the 2-D Schnakenberg model with localized heterogeneities. Zbl 1467.35045
Wong, Tony; Ward, Michael J.
2021
A novel approach to modelling the spatial spread of airborne diseases: an epidemic model with indirect transmission. Zbl 1467.92186
David, Jummy F.; Iyaniwura, Sarafa A.; Ward, Michael J.; Brauer, Fred
2020
Weakly nonlinear theory for oscillatory dynamics in a one-dimensional PDE-ODE model of membrane dynamics coupled by a bulk diffusion field. Zbl 1446.37071
Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J.
2020
Weakly nonlinear analysis of peanut-shaped deformations for localized spots of singularly perturbed reaction-diffusion systems. Zbl 1472.35026
Wong, Tony; Ward, Michael J.
2020
Stable asymmetric spike equilibria for the Gierer-Meinhardt model with a precursor field. Zbl 1460.35014
Kolokolnikov, Theodore; Paquin-Lefebvre, Frédéric; Ward, Michael J.
2020
The linear stability of symmetric spike patterns for a bulk-membrane coupled Gierer-Meinhardt model. Zbl 1419.35107
Gomez, Daniel; Ward, Michael J.; Wei, Juncheng
2019
Pattern formation and oscillatory dynamics in a two-dimensional coupled bulk-surface reaction-diffusion system. Zbl 1428.37071
Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J.
2019
Refined stability thresholds for localized spot patterns for the Brusselator model in $$\mathbb{R}^2$$. Zbl 1427.35107
Chang, Yifan; Tzou, J. C.; Ward, M. J.; Wei, J. C.
2019
Spots, traps, and patches: asymptotic analysis of localized solutions to some linear and nonlinear diffusive systems. Zbl 1393.35106
Ward, M. J.
2018
The stability and slow dynamics of spot patterns in the 2D Brusselator model: the effect of open systems and heterogeneities. Zbl 1392.35039
Tzou, J. C.; Ward, M. J.
2018
Spot dynamics in a reaction-diffusion model of plant root hair initiation. Zbl 1383.92048
Avitabile, Daniele; Breña-Medina, Victor F.; Ward, Michael J.
2018
Asynchronous instabilities of crime hotspots for a 1-D reaction-diffusion model of urban crime with focused police patrol. Zbl 1397.35138
Tse, Wang Hung; Ward, Michael J.
2018
Anomalous scaling of Hopf bifurcation thresholds for the stability of localized spot patterns for reaction-diffusion systems in two dimensions. Zbl 1391.35225
Tzou, J. C.; Ward, M. J.; Wei, J. C.
2018
Stabilizing a homoclinic stripe. Zbl 1425.35100
Kolokolnikov, Theodore; Ward, Michael; Tzou, Justin; Wei, Juncheng
2018
A time-delay in the activator kinetics enhances the stability of a spike solution to the Gierer-Meinhardt model. Zbl 1395.37055
Fadai, Nabil T.; Ward, Michael J.; Wei, Juncheng
2018
First passage statistics for the capture of a Brownian particle by a structured spherical target with multiple surface traps. Zbl 1372.35021
Lindsay, Alan E.; Bernoff, Andrew J.; Ward, Michael J.
2017
The stability and slow dynamics of localized spot patterns for the 3-D Schnakenberg reaction-diffusion model. Zbl 1434.35019
Tzou, J. C.; Xie, S.; Kolokolnikov, T.; Ward, M. J.
2017
A theory of synchrony by coupling through a diffusive chemical signal. Zbl 1376.92020
Gou, Jia; Chiang, Wei-Yin; Lai, Pik-Yin; Ward, Michael J.; Li, Yue-Xian
2017
Delayed reaction kinetics and the stability of spikes in the Gierer-Meinhardt model. Zbl 1368.35021
Fadai, Nabil T.; Ward, Michael J.; Wei, Juncheng
2017
Existence, stability, and dynamics of ring and near-ring solutions to the saturated Gierer-Meinhardt model in the semistrong regime. Zbl 1434.35017
Moyles, Iain R.; Ward, Michael J.
2017
Transition to blow-up in a reaction-diffusion model with localized spike solutions. Zbl 1387.35338
Rottschäfer, V.; Tzou, J. C.; Ward, M. J.
2017
Application of quasi-steady-state methods to nonlinear models of intracellular transport by molecular motors. Zbl 1372.92035
Zmurchok, Cole; Small, Tim; Ward, Michael J.; Edelstein-Keshet, Leah
2017
A hybrid asymptotic-numerical method for calculating drag coefficients in 2-D low Reynolds number flows. Zbl 1365.76273
Hormozi, Sarah; Ward, Michael J.
2017
An asymptotic analysis of a 2-D model of dynamically active compartments coupled by bulk diffusion. Zbl 1439.92024
Gou, J.; Ward, M. J.
2016
The dynamics of localized spot patterns for reaction-diffusion systems on the sphere. Zbl 1338.35248
Trinh, Philippe H.; Ward, Michael J.
2016
Hotspot formation and dynamics for a continuum model of urban crime. Zbl 1408.91169
Tse, W. H.; Ward, M. J.
2016
Oscillatory dynamics for a coupled membrane-bulk diffusion model with Fitzhugh-Nagumo membrane kinetics. Zbl 1347.35032
Gou, J.; Ward, M. J.
2016
Explicitly solvable nonlocal eigenvalue problems and the stability of localized stripes in reaction-diffusion systems. Zbl 1338.35246
Moyles, I.; Tse, W. H.; Ward, M. J.
2016
Mathematical modelling of crime and security: special issue of EJAM. Zbl 1384.00059
2016
Localized spot patterns on the sphere for reaction-diffusion systems: theory and open problems. Zbl 1357.35189
Jamieson-Lane, Alastair; Trinh, Philippe H.; Ward, Michael J.
2016
Slowly varying control parameters, delayed bifurcations, and the stability of spikes in reaction-diffusion systems. Zbl 1364.35151
Tzou, J. C.; Ward, M. J.; Kolokolnikov, T.
2015
Asymptotic analysis of first passage time problems inspired by ecology. Zbl 1319.35275
Kurella, Venu; Tzou, Justin; Coombs, Daniel; Ward, Michael
2015
Conditional mean first passage times to small traps in a 3-D domain with a sticky boundary: applications to T cell searching behavior in lymph nodes. Zbl 1339.92009
Delgado, M. I.; Ward, M. J.; Coombs, D.
2015
Synchronized oscillatory dynamics for a 1-D model of membrane kinetics coupled by linear bulk diffusion. Zbl 1331.35038
Gou, J.; Li, Y. X.; Nagata, W.; Ward, M. J.
2015
Stripe to spot transition in a plant root hair initiation model. Zbl 06444870
Breña-Medina, V. F.; Avitabile, D.; Champneys, A. R.; Ward, M. J.
2015
On accurately estimating stability thresholds for periodic spot patterns of reaction-diffusion systems in $$\mathbb{R}^2$$. Zbl 1382.35134
Iron, D.; Rumsey, J.; Ward, M. J.; Wei, J.
2015
The transition to a point constraint in a mixed biharmonic eigenvalue problem. Zbl 1319.35120
Lindsay, A. E.; Ward, M. J.; Kolokolnikov, T.
2015
The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime. Zbl 1304.35051
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2014
The stability of localized spot patterns for the Brusselator on the sphere. Zbl 1302.35033
Rozada, Ignacio; Ruuth, Steven J.; Ward, M. J.
2014
Logarithmic expansions and the stability of periodic patterns of localized spots for reaction-diffusion systems in $$\mathbb R^2$$. Zbl 1334.35347
Iron, David; Rumsey, John; Ward, Michael J.; Wei, Juncheng
2014
Mathematical modeling of plant root hair initiation: dynamics of localized patches. Zbl 1302.35030
Breña-Medina, V.; Champneys, A. R.; Grierson, C.; Ward, M. J.
2014
An explicitly solvable nonlocal eigenvalue problem and the stability of a spike for a sub-diffusive reaction-diffusion system. Zbl 1275.35020
Nec, Y.; Ward, M. J.
2013
The stability of localized spikes for the 1-D Brusselator reaction-diffusion model. Zbl 1295.35038
Tzou, J. C.; Nec, Y.; Ward, M. J.
2013
The stability and slow dynamics of two-spike patterns for a class of reaction-diffusion system. Zbl 1283.35113
Nec, Y.; Ward, M. J.
2013
Dynamics and stability of spike-type solutions to a one dimensional Gierer-Meinhardt model with sub-diffusion. Zbl 1252.35033
Nec, Yana; Ward, Michael J.
2012
The stability and dynamics of localized spot patterns in the two-dimensional Gray-Scott model. Zbl 1223.35033
Chen, W.; Ward, M. J.
2011
Optimizing the principal eigenvalue of the Laplacian in a sphere with interior traps. Zbl 1219.35155
Cheviakov, A. F.; Ward, M. J.
2011
Asymptotics of some nonlinear eigenvalue problems modelling a MEMS capacitor. II: Multiple solutions and singular asymptotics. Zbl 1220.35108
Lindsay, A. E.; Ward, M. J.
2011
Asymptotic analysis of localized solutions to some linear and nonlinear biharmonic eigenvalue problems. Zbl 1219.35043
Kropinski, M. C.; Lindsay, A. E.; Ward, M. J.
2011
Nonlinear dynamics of a periodically driven Duffing resonator coupled to a van der Pol oscillator. Zbl 1250.34032
Wei, X.; Randrianandrasana, M. F.; Ward, M.; Lowe, D.
2011
An asymptotic analysis of the mean first passage time for narrow escape problems. I: Two-dimensional domains. Zbl 1203.35023
Pillay, S.; Ward, M. J.; Peirce, A.; Kolokolnikov, T.
2010
An asymptotic analysis of the mean first passage time for narrow escape problems. II: The sphere. Zbl 1204.35030
Cheviakov, Alexei F.; Ward, Michael J.; Straube, Ronny
2010
Similarity: Generalizations, applications and open problems. Zbl 1188.00015
Bluman, G.; Broadbridge, P.; King, J. R.; Ward, M. J.
2010
An asymptotic analysis of the persistence threshold for the diffusive logistic model in spatial environments with localized patches. Zbl 1207.35035
Lindsay, Alan E.; Ward, Michael J.
2010
Asymptotic methods for PDE problems in fluid mechanics and related systems with strong localized perturbations in two dimensional domains. Zbl 1419.76535
Ward, Michael J.; Kropinski, Mary-Catherine
2010
Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain. Zbl 1178.35039
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2009
Diffusion on a sphere with localized traps: mean first passage time, eigenvalue asymptotics, and Fekete points. Zbl 1191.35032
Coombs, Daniel; Straube, Ronny; Ward, Michael
2009
Oscillatory instabilities and dynamics of multi-spike patterns for the one-dimensional Gray-Scott model. Zbl 1197.35021
Chen, Wan; Ward, Michael J.
2009
An asymptotic analysis of intracellular signaling gradients arising from multiple small compartments. Zbl 1182.92025
Straube, Ronny; Ward, Michael J.
2009
Asymptotics of some nonlinear eigenvalue problems for a MEMS capacitor: Part I: Fold point asymptotics. Zbl 1173.35625
Lindsay, A. E.; Ward, M. J.
2008
Diffusion of protein receptors on a cylindrical dendritic membrane with partially absorbing traps. Zbl 1146.92005
Bressloff, Paul C.; Earnshaw, Berton A.; Ward, Michael J.
2008
The stability and dynamics of a spike in the 1D Keller-Segel model. Zbl 1133.35058
Kang, K.; Kolokolnikov, T.; Ward, M. J.
2007
Self-replication of mesa patterns in reaction-diffusion systems. Zbl 1136.35002
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2007
Reaction rate of small diffusing molecules on a cylindrical membrane. Zbl 1206.82150
Straube, Ronny; Ward, Michael J.; Falcke, Martin
2007
A two-dimensional metastable flame-front and a degenrate spike-layer problem. Zbl 1140.35336
Cheviakov, Alexei F.; Ward, Michael J.
2007
The stability of a stripe for the Gierer-Meinhardt model and the effect of saturation. Zbl 1210.35016
Kolokolnikov, Theodore; Sun, Wentao; Ward, Michael; Wei, Juncheng
2006
Zigzag and breakup instabilities of stripes and rings in the two-dimensional Gray-Scott model. Zbl 1145.35388
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2006
Asymptotic methods for reaction-diffusion systems: past and present. Zbl 1334.92004
Ward, Michael J.
2006
Slow translational instabilities of spike patterns in the one-dimensional Gray-Scott model. Zbl 1105.35132
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2006
Touchdown and pull-in voltage behavior of a MEMS device with varying dielectric properties. Zbl 1103.35042
Guo, Yujin; Pan, Zhenguo; Ward, M. J.
2005
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime. Zbl 1136.35003
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: The low feed-rate regime. Zbl 1145.65328
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps. Zbl 1090.35070
Kolokolnikov, T.; Titcombe, M. S.; Ward, M. J.
2005
The existence and stability of spike patterns in a chemotaxis model. Zbl 1073.35118
Sleeman, B. D.; Ward, Michael J.; Wei, J. C.
2005
The slow dynamics of two-spike solutions for the Gray-Scott and Gierer-Meinhardt systems: competition and oscillatory instabilities. Zbl 1145.35404
Sun, Wentao; Ward, Michael J.; Russell, Robert
2005
The existence and stability of spike equilibria in the one-dimensional Gray – Scott model on a finite domain. Zbl 1125.35048
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Pulse-splitting for some reaction-diffusion systems in one-space dimension. Zbl 1145.35401
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Bifurcation of spike equilibria in the near-shadow Gierer-Meinhardt model. Zbl 1063.35084
Kolokolnikov, Theodore; Ward, Michael J.
2004
The stability and dynamics of hot-spot solutions to two one-dimensional microwave heating models. Zbl 1050.35008
Iron, David; Ward, Michael J.
2004
Spikes for singularly perturbed reaction-diffusion systems and Carrier’s problem. Zbl 1125.35373
Ward, Michael J.
2004
Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model. Zbl 1030.35011
Ward, M. J.; Wei, J.
2003
Hopf bifurction of spike solutions for the shadow Gierer-Meinhardt model. Zbl 1063.35030
Ward, M. J.; Wei, J.
2003
Reduced wave Green’s functions and their effect on the dynamics of a spike for the Gierer-Meinhardt model. Zbl 1063.35024
Kolokolnikov, Theodore; Ward, Michael J.
2003
Numerical challenges for resolving spike dynamics for two one-dimensional reaction-diffusion systems. Zbl 1141.35389
Sun, Wentao; Tang, Tao; Ward, Michael J.; Wei, Juncheng
2003
The analysis of a two-phase zone with condensation in a porous medium. Zbl 1113.76458
Bridge, L.; Bradean, R.; Ward, M. J.; Wetton, B. R.
2003
The existence and stability of asymmetric spike patterns for the Schnakenberg model. Zbl 1152.35397
Ward, Michael J.; Wei, Juncheng
2002
The dynamics of multispike solutions to the one-dimensional Gierer-Meinhardt model. Zbl 1019.35016
Iron, David; Ward, Michael J.
2002
Asymmetric spike patterns for the one-dimensional Gierer-Meinhardt model: Equilibria and stability. Zbl 1010.35002
Ward, M. J.; Wei, J.
2002
The dynamics and pinning of a spike for a reaction-diffusion system. Zbl 1032.35029
Ward, Michael J.; McInerney, Darragh; Houston, Paul; Gavaghan, David; Maini, Philip
2002
A practical method for finite element ring rolling simulation using the ALE flow formulation. Zbl 1125.74383
Davey, K.; Ward, M. J.
2002
Thermal runaway and microwave heating in thin cylindrical domains. Zbl 1002.80010
Ward, Michael J.
2002
The stability of spike solutions to the one-dimensional Gierer-Meinhardt model. Zbl 0983.35020
Iron, David; Ward, Michael J.; Wei, Juncheng
2001
Metastable dynamics and exponential asymptotics in multi-dimensional domains. Zbl 1007.35002
Ward, Michael J.
2001
The dynamics of drops and attached interfaces for the constrained Allen-Cahn equation. Zbl 0988.76095
Stafford, D.; Ward, M. J.; Wetton, B.
2001
Spike pinning for the Gierer-Meinhardt model. Zbl 0979.35142
Iron, David; Ward, Michael J.
2001
A metastable spike solution for a nonlocal reaction-diffusion model. Zbl 0956.35011
Iron, David; Ward, Michael J.
2000
Dynamics and coarsening of interfaces for the viscous Cahn-Hilliard equation in one spatial dimension. Zbl 1136.74366
Sun, Xiaodi; Ward, Michael J.
2000
...and 33 more Documents
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### Cited by 950 Authors

 77 Ward, Michael J. 58 Wei, Juncheng 29 Kolokolnikov, Theodore 20 Winter, Matthias 18 Holcman, David 16 Doelman, Arjen 15 Lindsay, Alan E. 14 Tzou, Justin C. 13 Iron, David 11 Lanza de Cristoforis, Massimo 11 Laurençot, Philippe 11 Lawley, Sean D. 11 Strani, Marta 11 Walker, Christoph 10 Chen, Xinfu 9 Bressloff, Paul C. 9 Iyaniwura, Sarafa A. 8 Rademacher, Jens Diederich Michael 8 Schuss, Zeev 8 van Heijster, Peter 8 Wang, Mingxin 7 Nec, Yana 7 Zhou, Jun 6 Bertozzi, Andrea Louise 6 Folino, Raffaele 6 Horikawa, Yo 6 Ishii, Yuta 6 Maini, Philip Kumar 6 Wetton, Brian R. 5 Champneys, Alan R. 5 Escher, Joachim 5 Gomez, Daniel 5 Gou, Jia 5 Krause, Andrew L. 5 Madzvamuse, Anotida 5 Musolino, Paolo 5 Shi, Junping 5 Wu, Ranchao 5 Xie, Shuangquan 5 Zhang, Yajing 4 Ao, Weiwei 4 Bastiaansen, Robbin 4 Bernoff, Andrew J. 4 Breña-Medina, Víctor F. 4 Chen, Mengxin 4 Dalla Riva, Matteo 4 Fusco, Giorgio 4 Gaffney, Eamonn A. 4 Glasner, Karl B. 4 Grebenkov, Denis S. 4 Guo, Jong-Shenq 4 Guo, Zongming 4 Hao, Jianghao 4 Hou, Xiaojie 4 Klika, Václav 4 Kowalczyk, Michał 4 Kühn, Christian 4 Lai, Xin 4 Li, Tong 4 Li, You 4 Lienstromberg, Christina 4 Mascia, Corrado 4 Mei, Linfeng 4 Morimoto, Kotaro 4 Moyles, Iain R. 4 Nagata, Wayne 4 Nishiura, Yasumasa 4 Peng, Rui 4 Promislow, Keith Steven 4 Qin, Cong 4 Reyna, Luis Guillermo M. 4 Rumsey, John R. 4 Sandstede, Björn 4 Tarzia, Domingo Alberto 4 Tse, Wang Hung 4 Wang, Chuntian 4 Wang, Jinliang 4 Wang, Qi 4 Wang, Qi 4 Winkler, Michael 3 Ammari, Habib M. 3 Avitabile, Daniele 3 Bates, Peter W. 3 Boukrouche, Mahdi 3 Bramburger, Jason J. 3 Brubaker, Nicholas D. 3 Cartailler, J. 3 Carter, Paul M. 3 Chen, Liping 3 Chen, Miaochao 3 Chen, Wenyan 3 Chirilus-Bruckner, Martina 3 Choi, Yongho 3 Choo, S. M. 3 David, Jummy Funke 3 Fan, Jishan 3 Gai, Chunyi 3 Iuorio, Annalisa 3 Kaper, Tasso J. 3 Kavallaris, Nikos I. ...and 850 more Authors
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### Cited in 170 Serials

 44 Journal of Differential Equations 36 Physica D 29 European Journal of Applied Mathematics 27 SIAM Journal on Applied Dynamical Systems 25 SIAM Journal on Applied Mathematics 23 Journal of Mathematical Analysis and Applications 22 Journal of Mathematical Biology 22 Bulletin of Mathematical Biology 21 Journal of Nonlinear Science 17 Discrete and Continuous Dynamical Systems. Series B 16 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 14 Studies in Applied Mathematics 14 Journal of Dynamics and Differential Equations 14 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 13 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 12 Nonlinearity 12 Applied Mathematics Letters 11 Journal of Computational Physics 11 Discrete and Continuous Dynamical Systems 11 Multiscale Modeling & Simulation 10 Journal of Engineering Mathematics 10 Journal of Fluid Mechanics 9 Journal of Statistical Physics 9 Nonlinear Analysis. Real World Applications 8 Chaos 8 Communications in Nonlinear Science and Numerical Simulation 8 Discrete and Continuous Dynamical Systems. Series S 7 Computers & Mathematics with Applications 7 Applied Mathematics and Computation 7 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Mathematical and Computer Modelling 6 Communications on Pure and Applied Analysis 6 Complex Variables and Elliptic Equations 5 Physica A 5 Acta Applicandae Mathematicae 5 Journal of Scientific Computing 5 Mathematical Modelling of Natural Phenomena 4 Applicable Analysis 4 Mathematical Methods in the Applied Sciences 4 Chaos, Solitons and Fractals 4 Applied Mathematical Modelling 4 SIAM Journal on Mathematical Analysis 4 SIAM Journal on Scientific Computing 4 Calculus of Variations and Partial Differential Equations 4 Mathematical Biosciences and Engineering 4 Journal of Theoretical Biology 3 Archive for Rational Mechanics and Analysis 3 Journal of Mathematical Physics 3 Journal of Computational and Applied Mathematics 3 Numerical Functional Analysis and Optimization 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Applied Numerical Mathematics 3 Japan Journal of Industrial and Applied Mathematics 3 International Journal of Computer Mathematics 3 NoDEA. Nonlinear Differential Equations and Applications 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Boundary Value Problems 3 Communications in Computational Physics 3 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Mathematical Biosciences 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Duke Mathematical Journal 2 Mathematics and Computers in Simulation 2 Proceedings of the American Mathematical Society 2 Quarterly of Applied Mathematics 2 Transactions of the American Mathematical Society 2 Acta Mathematicae Applicatae Sinica. English Series 2 Journal of Complexity 2 Neural Networks 2 SIAM Review 2 Physics of Fluids 2 Journal of Mathematical Chemistry 2 Nonlinear Dynamics 2 Abstract and Applied Analysis 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Discrete Dynamics in Nature and Society 2 Analysis (München) 2 Combustion Theory and Modelling 2 Communications in Contemporary Mathematics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Applied Mathematics and Computing 2 Advances in Difference Equations 2 Journal of Statistical Mechanics: Theory and Experiment 2 Waves in Random and Complex Media 2 Journal of Physics A: Mathematical and Theoretical 2 Networks and Heterogeneous Media 2 Science China. Mathematics 2 The Journal of Mathematical Neuroscience 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 2 Journal of Elliptic and Parabolic Equations 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Acta Mechanica 1 Communications in Mathematical Physics 1 Computer Methods in Applied Mechanics and Engineering 1 Computer Physics Communications 1 Communications on Pure and Applied Mathematics 1 International Journal of Engineering Science 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Physics Reports 1 Reviews of Modern Physics ...and 70 more Serials
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### Cited in 40 Fields

 563 Partial differential equations (35-XX) 244 Biology and other natural sciences (92-XX) 82 Numerical analysis (65-XX) 80 Ordinary differential equations (34-XX) 56 Fluid mechanics (76-XX) 54 Dynamical systems and ergodic theory (37-XX) 49 Probability theory and stochastic processes (60-XX) 46 Mechanics of deformable solids (74-XX) 36 Statistical mechanics, structure of matter (82-XX) 26 Optics, electromagnetic theory (78-XX) 22 Operator theory (47-XX) 21 Classical thermodynamics, heat transfer (80-XX) 20 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Integral equations (45-XX) 13 Global analysis, analysis on manifolds (58-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 9 Potential theory (31-XX) 8 Mechanics of particles and systems (70-XX) 6 Quantum theory (81-XX) 5 Differential geometry (53-XX) 4 Systems theory; control (93-XX) 3 Functions of a complex variable (30-XX) 3 Approximations and expansions (41-XX) 3 Functional analysis (46-XX) 3 Statistics (62-XX) 3 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Real functions (26-XX) 2 Special functions (33-XX) 2 Difference and functional equations (39-XX) 1 Topological groups, Lie groups (22-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) 1 Relativity and gravitational theory (83-XX) 1 Operations research, mathematical programming (90-XX) 1 Mathematics education (97-XX)