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Author ID: bates.peter-w Recent zbMATH articles by "Bates, Peter W."
Published as: Bates, Peter W.; Bates, P. W.; Bates, Peter
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Serials

11 Journal of Differential Equations
5 Transactions of the American Mathematical Society
5 SIAM Journal on Mathematical Analysis
4 Archive for Rational Mechanics and Analysis
4 Discrete and Continuous Dynamical Systems
3 Journal of Mathematical Analysis and Applications
3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
3 Physica D
3 Nonlinear Analysis. Theory, Methods & Applications
2 Communications in Mathematical Physics
2 Rocky Mountain Journal of Mathematics
2 Pacific Journal of Mathematics
2 Linear Algebra and its Applications
2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
2 Journal of Dynamics and Differential Equations
2 Electronic Journal of Differential Equations (EJDE)
2 Discrete and Continuous Dynamical Systems. Series B
2 SIAM Journal on Applied Dynamical Systems
2 Communications in Mathematical Sciences
1 Communications on Pure and Applied Mathematics
1 Houston Journal of Mathematics
1 Journal of Mathematical Biology
1 Journal of Mathematical Physics
1 Journal of Statistical Physics
1 Nonlinearity
1 International Journal of Mathematics and Mathematical Sciences
1 Inventiones Mathematicae
1 Journal of Computational and Applied Mathematics
1 Journal of Functional Analysis
1 Memoirs of the American Mathematical Society
1 Proceedings of the American Mathematical Society
1 Revista Colombiana de Matemáticas
1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
1 European Journal of Applied Mathematics
1 The Journal of Geometric Analysis
1 Communications in Partial Differential Equations
1 SIAM Journal on Applied Mathematics
1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
1 Journal of Nonlinear Science
1 The Canadian Applied Mathematics Quarterly
1 Calculus of Variations and Partial Differential Equations
1 Advances in Computational Mathematics
1 Advances in Differential Equations
1 RIMS Kokyuroku
1 Interfaces and Free Boundaries
1 Advanced Nonlinear Studies
1 Stochastics and Dynamics
1 International Journal of Numerical Analysis and Modeling
1 Mathematical Biosciences and Engineering
1 Networks and Heterogeneous Media
1 RIMS Kôkyûroku Bessatsu

Publications by Year

Citations contained in zbMATH Open

99 Publications have been cited 3,060 times in 1,872 Documents Cited by Year
Traveling waves in a convolution model for phase transitions. Zbl 0889.45012
Bates, Peter W.; Fife, Paul C.; Ren, Xiaofeng; Wang, Xuefeng
283
1997
Random attractors for stochastic reaction-diffusion equations on unbounded domains. Zbl 1155.35112
Bates, Peter W.; Lu, Kening; Wang, Bixiang
239
2009
Attractors for stochastic lattice dynamical systems. Zbl 1105.60041
Bates, Peter W.; Lisei, Hannelore; Lu, Kening
190
2006
Attractors for lattice dynamical systems. Zbl 1091.37515
Bates, Peter W.; Lu, Kening; Wang, Bixiang
155
2001
Convergence of the Cahn-Hilliard equation to the Hele-Shaw model. Zbl 0828.35105
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu
126
1994
Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal. Zbl 1114.35017
Bates, Peter W.; Zhao, Guangyu
111
2007
A discrete convolution model for phase transitions. Zbl 0956.74037
Bates, Peter W.; Chmaj, Adam
111
1999
An integrodifferential model for phase transitions: stationary solutions in higher space dimensions. Zbl 0958.82015
Bates, Peter W.; Chmaj, Adam
93
1999
Slow motion for the Cahn-Hilliard equation in one space dimension. Zbl 0753.35042
Alikakos, Nicholas; Bates, Peter W.; Fusco, Giorgio
90
1991
Traveling waves of bistable dynamics on a lattice. Zbl 1050.37041
Bates, Peter W.; Chen, Xinfu; Chmaj, Adam J. J.
87
2003
Periodic traveling waves and locating oscillating patterns in multidimensional domains. Zbl 0929.35067
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu
87
1999
On some nonlocal evolution equations arising in materials science. Zbl 1101.35073
Bates, Peter W.
81
2006
Attractors of non-autonomous stochastic lattice systems in weighted spaces. Zbl 1364.34113
Bates, Peter W.; Lu, Kening; Wang, Bixiang
77
2014
The dynamics of nucleation for the Cahn-Hilliard equation. Zbl 0788.35061
Bates, Peter W.; Fife, Paul C.
72
1993
Existence and persistence of invariant manifolds for semiflows in Banach space. Zbl 1023.37013
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
72
1998
The Neumann boundary problem for a nonlocal Cahn-Hilliard equation. Zbl 1081.45004
Bates, Peter W.; Han, Jianlong
60
2005
Dynamics of the 3-D fractional complex Ginzburg-Landau equation. Zbl 1328.35279
Lu, Hong; Bates, Peter W.; Lü, Shujuan; Zhang, Mingji
48
2015
Invariant manifolds for semilinear partial differential equations. Zbl 0674.58024
Bates, Peter W.; Jones, Christopher K. R. T.
43
1989
Equilibria with many nuclei for the Cahn-Hilliard equation. Zbl 0990.35016
Bates, Peter W.; Fusco, Giorgio
42
2000
Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability. Zbl 1157.35407
Bates, Peter W.; Dancer, E. Norman; Shi, Junping
42
1999
Approximately invariant manifolds and global dynamics of spike states. Zbl 1157.37013
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
41
2008
The Dirichlet boundary problem for a nonlocal Cahn-Hilliard equation. Zbl 1108.45004
Bates, Peter W.; Han, Jianlong
37
2005
Asymptotic behavior of stochastic fractional power dissipative equations on \(\mathbb{R}^n\). Zbl 1337.37062
Lu, Hong; Bates, Peter W.; Xin, Jie; Zhang, Mingji
36
2015
Inertial manifolds and inertial sets for the phase-field equations. Zbl 0758.35040
Bates, Peter W.; Zheng, Songmu
35
1992
Existence and instability of spike layer solutions to singular perturbation problems. Zbl 1010.47036
Bates, Peter W.; Shi, Junping
34
2002
Spectral comparison principles for the Cahn-Hilliard and phase-field equations, and time scales for coarsening. Zbl 0706.58074
Bates, Peter W.; Fife, Paul C.
34
1990
Metastable patterns for the Cahn-Hilliard equation. I. Zbl 0805.35046
Bates, Peter W.; Xun, Jianping
33
1994
Numerical analysis for a nonlocal Allen-Cahn equation. Zbl 1165.65051
Bates, Peter W.; Brown, Sarah; Han, Jianlong
32
2009
Metastable patterns for the Cahn-Hilliard equation. II: Layer dynamics and slow invariant manifold. Zbl 0821.35074
Bates, Peter W.; Xun, Jianping
32
1995
Dynamics of the 3D fractional Ginzburg-Landau equation with multiplicative noise on an unbounded domain. Zbl 1331.37070
Lu, Hong; Bates, Peter W.; Lü, Shujuan; Zhang, Mingji
31
2015
Invariant foliations near normally hyperbolic invariant manifolds for semiflows. Zbl 0964.37018
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
31
2000
Spectral analysis and multidimensional stability of traveling waves for nonlocal Allen–Cahn equation. Zbl 1121.35322
Bates, Peter W.; Chen, Fengxin
30
2002
Geometric and potential driving formation and evolution of biomolecular surfaces. Zbl 1311.92212
Bates, P. W.; Chen, Zhan; Sun, Yuhui; Wei, Guo-Wei; Zhao, Shan
30
2009
Persistence of overflowing manifolds for semiflow. Zbl 0947.37009
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
24
1999
Spectral analysis of traveling waves for nonlocal evolution equations. Zbl 1134.35060
Bates, Peter W.; Chen, Fengxin
24
2006
Heteroclinic solutions of a van der Waals model with infinite nonlocal interactions. Zbl 1086.49008
Bates, Peter W.; Chen, Xinfu; Chmaj, Adam J. J.
23
2005
Periodic traveling waves for a nonlocal integro-differential model. Zbl 0924.35060
Bates, Peter; Chen, Fengxin
20
1999
Tempered random attractors for parabolic equations in weighted spaces. Zbl 1288.35097
Bates, Peter W.; Lu, Kening; Wang, Bixiang
19
2013
On the singular limit in a phase field model of phase transitions. Zbl 0696.35060
Alikakos, Nicholas D.; Bates, Peter W.
19
1988
The existence of travelling wave solutions of a generalized phase-field model. Zbl 0867.35041
Bates, P. W.; Fife, P. C.; Gardner, R. A.; Jones, C. K. R. T.
18
1997
Nucleation of instability of the Meissner state of 3-dimensional superconductors. Zbl 1137.82024
Bates, Peter W.; Pan, Xing-Bin
17
2007
Periodic solutions of higher order systems. Zbl 0424.34042
Bates, P. W.; Ward, J. R.
16
1979
Solutions to the nonautonomous bistable equation with specified Morse index. I: Existence. Zbl 0788.34012
Alikakos, Nicholas D.; Bates, Peter W.; Fusco, Giorgio
15
1993
Blow up for a diffusion-advection equation. Zbl 0707.35018
Alikakos, Nicholas D.; Bates, Peter W.; Grant, Christopher P.
15
1989
Motion of a droplet for the stochastic mass-conserving Allen-Cahn equation. Zbl 1439.35232
Antonopoulou, D. C.; Bates, P. W.; Blömker, D.; Karali, G. D.
14
2016
Individual flux study via steady-state Poisson-Nernst-Planck systems: effects from boundary conditions. Zbl 1434.34040
Bates, Peter W.; Jia, Yusheng; Lin, Guojian; Lu, Hong; Zhang, Mingji
14
2017
On a nonlocal phase-field system. Zbl 1092.35010
Bates, Peter W.; Han, Jianlong; Zhao, Guangyu
14
2006
Ion size and valence effects on ionic flows via Poisson-Nernst-Planck models. Zbl 1367.76071
Bates, Peter W.; Liu, Weishi; Lu, Hong; Zhang, Mingji
14
2017
A Hartman-Grobman theorem for the Cahn-Hilliard and phase-field equations. Zbl 0795.35052
Bates, Peter W.; Lu, Kening
13
1994
Normally hyperbolic invariant manifolds for random dynamical systems. I: Persistence. Zbl 1291.37093
Li, Ji; Lu, Kening; Bates, Peter
13
2013
Solutions of nonlinear elliptic systems with meshed spectra. Zbl 0456.35050
Bates, Peter W.
11
1980
Existence and uniqueness for a variational hyperbolic system without resonance. Zbl 0456.35051
Bates, Peter W.; Castro, Alfonso
11
1980
Invariant foliations for random dynamical systems. Zbl 1351.37215
Li, Ji; Lu, Kening; Bates, Peter W.
11
2014
Traveling pulses for the Klein-Gordon equation on a lattice or continuum with long-range interaction. Zbl 1119.34034
Bates, Peter W.; Zhang, Chunlei
11
2006
Global dynamics of boundary droplets. Zbl 1315.37049
Bates, Peter W.; Jin, Jiayin
10
2014
Analysis of a corner layer problem in anisotropic interfaces. Zbl 1235.74011
Alikakos, N. D.; Bates, P. W.; Cahn, J. W.; Fife, P. C.; Fusco, G.; Tanoglu, G. B.
9
2006
Containment for weakly coupled parabolic systems. Zbl 0581.35036
Bates, P. W.
9
1985
Mathematical studies of Poisson-Nernst-Planck model for membrane channels: finite ion size effects without electroneutrality boundary conditions. Zbl 1420.34072
Aitbayev, Rakhim; Bates, Peter W.; Lu, Hong; Zhang, Lijun; Zhang, Mingji
8
2019
Phase field models for hypercooled solidification. Zbl 0890.35161
Bates, P. W.; Fife, P. C.; Gardner, R. A.; Jones, C. K. R. T.
8
1997
Global existence and uniqueness of solutions to a nonlocal phase-field system. Zbl 0938.35035
Bates, Peter W.; Chen, Fengxin; Wang, Junping
7
1997
Erratum: Nucleation of instability of the Meissner state of 3-dimensional superconductors. Zbl 1151.82439
Bates, Peter; Pan, Xing-Bin
7
2008
Bifurcation and stability of periodic traveling waves for a reaction- diffusion system. Zbl 0494.35056
Barrow, David L.; Bates, Peter W.
6
1983
Geometric singular perturbation theory with real noise. Zbl 1332.34099
Li, Ji; Lu, Kening; Bates, Peter W.
6
2015
Multiphase solutions to the vector Allen-Cahn equation: crystalline and other complex symmetric structures. Zbl 1375.35538
Bates, Peter W.; Fusco, Giorgio; Smyrnelis, Panayotis
6
2017
Transition layer solutions of a higher order equation in an infinite tube. Zbl 0904.35019
Bates, Peter W.; Ren, Xiaofeng
6
1996
Mullins-Sekerka motion of small droplets on a fixed boundary. Zbl 0984.35013
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu; Fusco, Giorgio
6
2000
Stabilization of solutions for a class of degenerate equations in divergence form in one space dimension. Zbl 0671.35006
Alikakos, Nicholas D.; Bates, Peter W.
6
1988
Entire solutions with six-fold junctions to elliptic gradient systems with triangle symmetry. Zbl 1277.35157
Bates, Peter; Fusco, Giorgio; Smyrnelis, Panayotis
5
2013
Green’s function inequalities for two-point boundary value problems. Zbl 0299.34021
Bates, P. W.; Gustafson, G. B.
5
1975
Maximization of Green’s function over classes of multipoint boundary value problems. Zbl 0347.34011
Bates, P. W.; Gustafson, G. B.
5
1976
Small permanent charge effects on individual fluxes via Poisson-Nernst-Planck models with multiple cations. Zbl 1472.34086
Bates, Peter W.; Wen, Zhenshu; Zhang, Mingji
4
2021
Gradient dynamics: motion near a manifold of quasi-equilibria. Zbl 1409.37076
Bates, Peter; Fusco, Giorgio; Karali, Georgia
4
2018
Slow motion manifolds for a class of singular perturbation problems: The linearized equations. Zbl 0808.35058
Alikakos, N. D.; Bates, P. W.; Fusco, G.
4
1992
Hilbert space methods for nonlinear elliptic equations. Zbl 0365.34072
Bates, Peter W.
4
1979
Heteroclinic orbits for a higher order phase transition problem. Zbl 0873.35099
Bates, Peter W.; Ren, Xiaofeng
4
1997
Effects on \(I-V\) relations from small permanent charge and channel geometry via classical Poisson-Nernst-Planck equations with multiple cations. Zbl 1472.34099
Wen, Zhenshu; Bates, Peter W.; Zhang, Mingji
4
2021
Dynamics of ionic flows via Poisson-Nernst-Planck systems with local hard-sphere potentials: competition between cations. Zbl 1467.92254
Bates, Peter W.; Chen, Jianing; Zhang, Mingji
4
2020
Singular fold with real noise. Zbl 1366.37120
Zhang, Mingji; Li, Ji; Bates, Peter W.
3
2016
Traveling wave solutions for a nonlocal phase-field system. Zbl 1010.35107
Bates, Peter W.; Chen, Fengxin
3
2002
Estimates for the eigenvalues of the Jordan product of Hermitian matrices. Zbl 0539.15009
Alikakos, N.; Bates, P. W.
3
1984
Growth regulation and the insulin signaling pathway. Zbl 1263.92013
Bates, Peter W.; Liang, Yu; Shingleton, Alexander W.
3
2013
Invariant manifolds of interior multi-spike states for the Cahn-Hilliard equation in higher space dimensions. Zbl 1372.35019
Bates, Peter W.; Fusco, Giorgio; Jin, Jiayin
3
2017
Convergence to equilibrium in a reaction-diffusion system. Zbl 0555.35064
Bates, P. W.; Brown, K. J.
3
1984
Reduction theorems for a class of semilinear equations at resonance. Zbl 0496.47052
Bates, Peter W.
2
1982
Coarsening and nucleation in the Cahn-Hilliard equation. Zbl 0841.35130
Bates, P. W.
2
1993
Persistence of \(C^k\) normally hyperbolic invariant manifolds for infinite dimensional dynamical systems. Zbl 1288.37028
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
2
2001
Invariant foliations of overflowing manifolds for semiflows in Banach space. Zbl 0971.37015
Bates, Peter; Lu, Kening; Zeng, Chongchun
2
1999
A saddle-point theorem. Zbl 0599.34039
Bates, Peter W.; Ekeland, Ivar
2
1980
Approximate normally hyperbolic invariant manifolds for semiflows. Zbl 0959.34036
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
2
2000
Equilibria and traveling waves for bistable equations with non-local and discrete dissipation. Zbl 1058.35520
Bates, Peter W.; Chen, Xinfu; Chmaj, Adam
2
2000
The solutions of the nonlinear Klein-Gordon equation near a steady state. Zbl 0696.35142
Bates, P. W.; Jones, C. K. R. T.
2
1989
Necessary and sufficient conditions for existence of solutions to equations with noninvertible linear part. Zbl 0473.47048
Bates, Peter W.; Castro, Alfonso
1
1981
Bifurcation of periodic travelling waves for a reaction-diffuion system. Zbl 0508.35044
Barrow, D. L.; Bates, P. W.
1
1982
Neck-linker tension and the locomotion of kinesin along microtubules. Zbl 1216.92039
Bates, Peter W.; Jia, Zhiyuan
1
2010
Normally hyperbolic invariant manifolds for semiflow in a Banach space. Zbl 0972.37016
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
1
1997
Projection methods for nonlinear nodal problems. Zbl 0366.34009
Bates, P. W.; Gustafson, G. B.
1
1977
A numerical scheme for the Mullins-Sekerka evolution in three space dimensions. Zbl 0960.65113
Bates, Peter W.; Brown, Sarah
1
2000
An invariance principle for a class of monotone systems and application to degenerate parabolic equations. Zbl 0674.35044
Alikakos, N. D.; Bates, P. W.
1
1988
Travelling waves in radially symmetric parabolic systems. Zbl 0567.35045
Bates, Peter W.
1
1985
Small permanent charge effects on individual fluxes via Poisson-Nernst-Planck models with multiple cations. Zbl 1472.34086
Bates, Peter W.; Wen, Zhenshu; Zhang, Mingji
4
2021
Effects on \(I-V\) relations from small permanent charge and channel geometry via classical Poisson-Nernst-Planck equations with multiple cations. Zbl 1472.34099
Wen, Zhenshu; Bates, Peter W.; Zhang, Mingji
4
2021
Dynamics of ionic flows via Poisson-Nernst-Planck systems with local hard-sphere potentials: competition between cations. Zbl 1467.92254
Bates, Peter W.; Chen, Jianing; Zhang, Mingji
4
2020
Mathematical studies of Poisson-Nernst-Planck model for membrane channels: finite ion size effects without electroneutrality boundary conditions. Zbl 1420.34072
Aitbayev, Rakhim; Bates, Peter W.; Lu, Hong; Zhang, Lijun; Zhang, Mingji
8
2019
Gradient dynamics: motion near a manifold of quasi-equilibria. Zbl 1409.37076
Bates, Peter; Fusco, Giorgio; Karali, Georgia
4
2018
Individual flux study via steady-state Poisson-Nernst-Planck systems: effects from boundary conditions. Zbl 1434.34040
Bates, Peter W.; Jia, Yusheng; Lin, Guojian; Lu, Hong; Zhang, Mingji
14
2017
Ion size and valence effects on ionic flows via Poisson-Nernst-Planck models. Zbl 1367.76071
Bates, Peter W.; Liu, Weishi; Lu, Hong; Zhang, Mingji
14
2017
Multiphase solutions to the vector Allen-Cahn equation: crystalline and other complex symmetric structures. Zbl 1375.35538
Bates, Peter W.; Fusco, Giorgio; Smyrnelis, Panayotis
6
2017
Invariant manifolds of interior multi-spike states for the Cahn-Hilliard equation in higher space dimensions. Zbl 1372.35019
Bates, Peter W.; Fusco, Giorgio; Jin, Jiayin
3
2017
Motion of a droplet for the stochastic mass-conserving Allen-Cahn equation. Zbl 1439.35232
Antonopoulou, D. C.; Bates, P. W.; Blömker, D.; Karali, G. D.
14
2016
Singular fold with real noise. Zbl 1366.37120
Zhang, Mingji; Li, Ji; Bates, Peter W.
3
2016
Dynamics of the 3-D fractional complex Ginzburg-Landau equation. Zbl 1328.35279
Lu, Hong; Bates, Peter W.; Lü, Shujuan; Zhang, Mingji
48
2015
Asymptotic behavior of stochastic fractional power dissipative equations on \(\mathbb{R}^n\). Zbl 1337.37062
Lu, Hong; Bates, Peter W.; Xin, Jie; Zhang, Mingji
36
2015
Dynamics of the 3D fractional Ginzburg-Landau equation with multiplicative noise on an unbounded domain. Zbl 1331.37070
Lu, Hong; Bates, Peter W.; Lü, Shujuan; Zhang, Mingji
31
2015
Geometric singular perturbation theory with real noise. Zbl 1332.34099
Li, Ji; Lu, Kening; Bates, Peter W.
6
2015
Attractors of non-autonomous stochastic lattice systems in weighted spaces. Zbl 1364.34113
Bates, Peter W.; Lu, Kening; Wang, Bixiang
77
2014
Invariant foliations for random dynamical systems. Zbl 1351.37215
Li, Ji; Lu, Kening; Bates, Peter W.
11
2014
Global dynamics of boundary droplets. Zbl 1315.37049
Bates, Peter W.; Jin, Jiayin
10
2014
Tempered random attractors for parabolic equations in weighted spaces. Zbl 1288.35097
Bates, Peter W.; Lu, Kening; Wang, Bixiang
19
2013
Normally hyperbolic invariant manifolds for random dynamical systems. I: Persistence. Zbl 1291.37093
Li, Ji; Lu, Kening; Bates, Peter
13
2013
Entire solutions with six-fold junctions to elliptic gradient systems with triangle symmetry. Zbl 1277.35157
Bates, Peter; Fusco, Giorgio; Smyrnelis, Panayotis
5
2013
Growth regulation and the insulin signaling pathway. Zbl 1263.92013
Bates, Peter W.; Liang, Yu; Shingleton, Alexander W.
3
2013
Neck-linker tension and the locomotion of kinesin along microtubules. Zbl 1216.92039
Bates, Peter W.; Jia, Zhiyuan
1
2010
Random attractors for stochastic reaction-diffusion equations on unbounded domains. Zbl 1155.35112
Bates, Peter W.; Lu, Kening; Wang, Bixiang
239
2009
Numerical analysis for a nonlocal Allen-Cahn equation. Zbl 1165.65051
Bates, Peter W.; Brown, Sarah; Han, Jianlong
32
2009
Geometric and potential driving formation and evolution of biomolecular surfaces. Zbl 1311.92212
Bates, P. W.; Chen, Zhan; Sun, Yuhui; Wei, Guo-Wei; Zhao, Shan
30
2009
Approximately invariant manifolds and global dynamics of spike states. Zbl 1157.37013
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
41
2008
Erratum: Nucleation of instability of the Meissner state of 3-dimensional superconductors. Zbl 1151.82439
Bates, Peter; Pan, Xing-Bin
7
2008
Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal. Zbl 1114.35017
Bates, Peter W.; Zhao, Guangyu
111
2007
Nucleation of instability of the Meissner state of 3-dimensional superconductors. Zbl 1137.82024
Bates, Peter W.; Pan, Xing-Bin
17
2007
Attractors for stochastic lattice dynamical systems. Zbl 1105.60041
Bates, Peter W.; Lisei, Hannelore; Lu, Kening
190
2006
On some nonlocal evolution equations arising in materials science. Zbl 1101.35073
Bates, Peter W.
81
2006
Spectral analysis of traveling waves for nonlocal evolution equations. Zbl 1134.35060
Bates, Peter W.; Chen, Fengxin
24
2006
On a nonlocal phase-field system. Zbl 1092.35010
Bates, Peter W.; Han, Jianlong; Zhao, Guangyu
14
2006
Traveling pulses for the Klein-Gordon equation on a lattice or continuum with long-range interaction. Zbl 1119.34034
Bates, Peter W.; Zhang, Chunlei
11
2006
Analysis of a corner layer problem in anisotropic interfaces. Zbl 1235.74011
Alikakos, N. D.; Bates, P. W.; Cahn, J. W.; Fife, P. C.; Fusco, G.; Tanoglu, G. B.
9
2006
The Neumann boundary problem for a nonlocal Cahn-Hilliard equation. Zbl 1081.45004
Bates, Peter W.; Han, Jianlong
60
2005
The Dirichlet boundary problem for a nonlocal Cahn-Hilliard equation. Zbl 1108.45004
Bates, Peter W.; Han, Jianlong
37
2005
Heteroclinic solutions of a van der Waals model with infinite nonlocal interactions. Zbl 1086.49008
Bates, Peter W.; Chen, Xinfu; Chmaj, Adam J. J.
23
2005
Traveling waves of bistable dynamics on a lattice. Zbl 1050.37041
Bates, Peter W.; Chen, Xinfu; Chmaj, Adam J. J.
87
2003
Existence and instability of spike layer solutions to singular perturbation problems. Zbl 1010.47036
Bates, Peter W.; Shi, Junping
34
2002
Spectral analysis and multidimensional stability of traveling waves for nonlocal Allen–Cahn equation. Zbl 1121.35322
Bates, Peter W.; Chen, Fengxin
30
2002
Traveling wave solutions for a nonlocal phase-field system. Zbl 1010.35107
Bates, Peter W.; Chen, Fengxin
3
2002
Attractors for lattice dynamical systems. Zbl 1091.37515
Bates, Peter W.; Lu, Kening; Wang, Bixiang
155
2001
Persistence of \(C^k\) normally hyperbolic invariant manifolds for infinite dimensional dynamical systems. Zbl 1288.37028
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
2
2001
Equilibria with many nuclei for the Cahn-Hilliard equation. Zbl 0990.35016
Bates, Peter W.; Fusco, Giorgio
42
2000
Invariant foliations near normally hyperbolic invariant manifolds for semiflows. Zbl 0964.37018
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
31
2000
Mullins-Sekerka motion of small droplets on a fixed boundary. Zbl 0984.35013
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu; Fusco, Giorgio
6
2000
Approximate normally hyperbolic invariant manifolds for semiflows. Zbl 0959.34036
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
2
2000
Equilibria and traveling waves for bistable equations with non-local and discrete dissipation. Zbl 1058.35520
Bates, Peter W.; Chen, Xinfu; Chmaj, Adam
2
2000
A numerical scheme for the Mullins-Sekerka evolution in three space dimensions. Zbl 0960.65113
Bates, Peter W.; Brown, Sarah
1
2000
A discrete convolution model for phase transitions. Zbl 0956.74037
Bates, Peter W.; Chmaj, Adam
111
1999
An integrodifferential model for phase transitions: stationary solutions in higher space dimensions. Zbl 0958.82015
Bates, Peter W.; Chmaj, Adam
93
1999
Periodic traveling waves and locating oscillating patterns in multidimensional domains. Zbl 0929.35067
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu
87
1999
Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability. Zbl 1157.35407
Bates, Peter W.; Dancer, E. Norman; Shi, Junping
42
1999
Persistence of overflowing manifolds for semiflow. Zbl 0947.37009
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
24
1999
Periodic traveling waves for a nonlocal integro-differential model. Zbl 0924.35060
Bates, Peter; Chen, Fengxin
20
1999
Invariant foliations of overflowing manifolds for semiflows in Banach space. Zbl 0971.37015
Bates, Peter; Lu, Kening; Zeng, Chongchun
2
1999
Existence and persistence of invariant manifolds for semiflows in Banach space. Zbl 1023.37013
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
72
1998
Traveling waves in a convolution model for phase transitions. Zbl 0889.45012
Bates, Peter W.; Fife, Paul C.; Ren, Xiaofeng; Wang, Xuefeng
283
1997
The existence of travelling wave solutions of a generalized phase-field model. Zbl 0867.35041
Bates, P. W.; Fife, P. C.; Gardner, R. A.; Jones, C. K. R. T.
18
1997
Phase field models for hypercooled solidification. Zbl 0890.35161
Bates, P. W.; Fife, P. C.; Gardner, R. A.; Jones, C. K. R. T.
8
1997
Global existence and uniqueness of solutions to a nonlocal phase-field system. Zbl 0938.35035
Bates, Peter W.; Chen, Fengxin; Wang, Junping
7
1997
Heteroclinic orbits for a higher order phase transition problem. Zbl 0873.35099
Bates, Peter W.; Ren, Xiaofeng
4
1997
Normally hyperbolic invariant manifolds for semiflow in a Banach space. Zbl 0972.37016
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
1
1997
Transition layer solutions of a higher order equation in an infinite tube. Zbl 0904.35019
Bates, Peter W.; Ren, Xiaofeng
6
1996
Metastable patterns for the Cahn-Hilliard equation. II: Layer dynamics and slow invariant manifold. Zbl 0821.35074
Bates, Peter W.; Xun, Jianping
32
1995
Convergence of the Cahn-Hilliard equation to the Hele-Shaw model. Zbl 0828.35105
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu
126
1994
Metastable patterns for the Cahn-Hilliard equation. I. Zbl 0805.35046
Bates, Peter W.; Xun, Jianping
33
1994
A Hartman-Grobman theorem for the Cahn-Hilliard and phase-field equations. Zbl 0795.35052
Bates, Peter W.; Lu, Kening
13
1994
The dynamics of nucleation for the Cahn-Hilliard equation. Zbl 0788.35061
Bates, Peter W.; Fife, Paul C.
72
1993
Solutions to the nonautonomous bistable equation with specified Morse index. I: Existence. Zbl 0788.34012
Alikakos, Nicholas D.; Bates, Peter W.; Fusco, Giorgio
15
1993
Coarsening and nucleation in the Cahn-Hilliard equation. Zbl 0841.35130
Bates, P. W.
2
1993
Inertial manifolds and inertial sets for the phase-field equations. Zbl 0758.35040
Bates, Peter W.; Zheng, Songmu
35
1992
Slow motion manifolds for a class of singular perturbation problems: The linearized equations. Zbl 0808.35058
Alikakos, N. D.; Bates, P. W.; Fusco, G.
4
1992
Slow motion for the Cahn-Hilliard equation in one space dimension. Zbl 0753.35042
Alikakos, Nicholas; Bates, Peter W.; Fusco, Giorgio
90
1991
Spectral comparison principles for the Cahn-Hilliard and phase-field equations, and time scales for coarsening. Zbl 0706.58074
Bates, Peter W.; Fife, Paul C.
34
1990
Invariant manifolds for semilinear partial differential equations. Zbl 0674.58024
Bates, Peter W.; Jones, Christopher K. R. T.
43
1989
Blow up for a diffusion-advection equation. Zbl 0707.35018
Alikakos, Nicholas D.; Bates, Peter W.; Grant, Christopher P.
15
1989
The solutions of the nonlinear Klein-Gordon equation near a steady state. Zbl 0696.35142
Bates, P. W.; Jones, C. K. R. T.
2
1989
On the singular limit in a phase field model of phase transitions. Zbl 0696.35060
Alikakos, Nicholas D.; Bates, Peter W.
19
1988
Stabilization of solutions for a class of degenerate equations in divergence form in one space dimension. Zbl 0671.35006
Alikakos, Nicholas D.; Bates, Peter W.
6
1988
An invariance principle for a class of monotone systems and application to degenerate parabolic equations. Zbl 0674.35044
Alikakos, N. D.; Bates, P. W.
1
1988
Containment for weakly coupled parabolic systems. Zbl 0581.35036
Bates, P. W.
9
1985
Travelling waves in radially symmetric parabolic systems. Zbl 0567.35045
Bates, Peter W.
1
1985
Estimates for the eigenvalues of the Jordan product of Hermitian matrices. Zbl 0539.15009
Alikakos, N.; Bates, P. W.
3
1984
Convergence to equilibrium in a reaction-diffusion system. Zbl 0555.35064
Bates, P. W.; Brown, K. J.
3
1984
Bifurcation and stability of periodic traveling waves for a reaction- diffusion system. Zbl 0494.35056
Barrow, David L.; Bates, Peter W.
6
1983
Reduction theorems for a class of semilinear equations at resonance. Zbl 0496.47052
Bates, Peter W.
2
1982
Bifurcation of periodic travelling waves for a reaction-diffuion system. Zbl 0508.35044
Barrow, D. L.; Bates, P. W.
1
1982
Necessary and sufficient conditions for existence of solutions to equations with noninvertible linear part. Zbl 0473.47048
Bates, Peter W.; Castro, Alfonso
1
1981
Solutions of nonlinear elliptic systems with meshed spectra. Zbl 0456.35050
Bates, Peter W.
11
1980
Existence and uniqueness for a variational hyperbolic system without resonance. Zbl 0456.35051
Bates, Peter W.; Castro, Alfonso
11
1980
A saddle-point theorem. Zbl 0599.34039
Bates, Peter W.; Ekeland, Ivar
2
1980
Periodic solutions of higher order systems. Zbl 0424.34042
Bates, P. W.; Ward, J. R.
16
1979
Hilbert space methods for nonlinear elliptic equations. Zbl 0365.34072
Bates, Peter W.
4
1979
Projection methods for nonlinear nodal problems. Zbl 0366.34009
Bates, P. W.; Gustafson, G. B.
1
1977
Maximization of Green’s function over classes of multipoint boundary value problems. Zbl 0347.34011
Bates, P. W.; Gustafson, G. B.
5
1976
Green’s function inequalities for two-point boundary value problems. Zbl 0299.34021
Bates, P. W.; Gustafson, G. B.
5
1975
all top 5

Cited by 1,815 Authors

68 Wang, Bixiang
60 Li, Wan-Tong
54 Zhou, Shengfan
41 Bates, Peter W.
39 Li, Yangrong
31 Lu, Kening
29 Shen, Wenxian
29 Wei, Juncheng
26 Rossi, Julio Daniel
25 Kloeden, Peter Eris
24 Wang, Renhai
23 Gu, Anhui
22 Han, Xiaoying
21 Zhang, Mingji
21 Zhao, Caidi
19 Caraballo Garrido, Tomás
19 Grasselli, Maurizio
19 Hupkes, Hermen Jan
19 Li, Dingshi
19 Shu, Ji
16 Du, Qiang
16 Ruan, Shigui
16 Yang, Feiying
15 Chen, Xinfu
15 Coville, Jerome
15 Fusco, Giorgio
15 Sun, Jianwen
15 Wang, Xiaohu
15 Wang, Zhaojuan
15 Wang, Zhi Cheng
14 Lin, Guo
14 Shi, Junping
14 Xu, Zhaoquan
14 Yuan, Rong
13 de la Llave, Rafael
13 Karali, Georgia D.
13 Pan, Xingbin
13 Wei, Guowei
13 Zhang, Guobao
12 Abdallah, Ahmed Y.
12 Alikakos, Nicholas D.
12 Du, Yihong
12 Shi, Lin
12 Zhao, Wenqiang
11 Abels, Helmut
11 Guo, Shangjiang
11 Strani, Marta
11 Valero, José
11 Van Vleck, Erik S.
11 Wang, Jiabing
11 Zhao, Shan
11 Zhao, Xiao-Qiang
10 Cortázar, Carmen
10 Gal, Ciprian Gheorghe Sorin
10 Lu, Hong
10 Miranville, Alain M.
10 Pan, Shuxia
10 Weng, Peixuan
10 Winter, Matthias
10 Wolanski, Noemi I.
10 Wu, Shiliang
9 Elgueta, Manuel
9 Li, Ji
9 Morillas, Francisco G.
9 Wang, Yejuan
9 Yang, Shuang
9 Zhang, Jian
8 Chen, Zhang
8 Cheng, Cuiping
8 Ei, Shin-Ichiro
8 Folino, Raffaele
8 Frigeri, Sergio
8 Kowalczyk, Michał
8 Li, Xiaojun
8 Nefedov, Nikolaĭ Nikolaevich
8 Novick-Cohen, Amy
8 Promislow, Keith Steven
8 Shen, Zhongwei
8 Sourdis, Christos
8 Sprekels, Jürgen
8 Yang, Xiaofeng
8 Zhao, Min
7 Bhowmik, Samir Kumar
7 Blömker, Dirk
7 Bogoya, Mauricio
7 Cheng, Hongmei
7 Chmaj, Adam J. J.
7 Cui, Hongyong
7 Du, Zengji
7 Gunzburger, Max D.
7 Guo, Boling
7 Hamel, François
7 Hsu, Cheng-Hsiung
7 Ju, Lili
7 Kühn, Christian
7 Li, Fuzhi
7 Martínez, Salomé
7 Quirós Gracián, Fernando
7 Schmalfuß, Björn
7 Shen, Jun
...and 1,715 more Authors
all top 5

Cited in 277 Serials

204 Journal of Differential Equations
87 Discrete and Continuous Dynamical Systems. Series B
81 Journal of Mathematical Analysis and Applications
67 Discrete and Continuous Dynamical Systems
64 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
61 Journal of Dynamics and Differential Equations
38 Communications on Pure and Applied Analysis
37 Applied Mathematics and Computation
31 Journal of Computational Physics
31 Physica D
30 Journal of Mathematical Physics
29 Archive for Rational Mechanics and Analysis
29 Calculus of Variations and Partial Differential Equations
27 Nonlinear Analysis. Real World Applications
26 Transactions of the American Mathematical Society
24 Computers & Mathematics with Applications
24 Proceedings of the American Mathematical Society
24 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
23 Nonlinearity
23 ZAMP. Zeitschrift für angewandte Mathematik und Physik
22 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
20 Abstract and Applied Analysis
20 Stochastics and Dynamics
19 Journal of Computational and Applied Mathematics
19 Applied Mathematics Letters
19 SIAM Journal on Mathematical Analysis
17 Journal of Scientific Computing
16 Journal of Difference Equations and Applications
14 Applicable Analysis
14 Journal of Mathematical Biology
14 Journal of Functional Analysis
14 Journal de Mathématiques Pures et Appliquées. Neuvième Série
14 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
14 SIAM Journal on Applied Dynamical Systems
13 Advances in Difference Equations
13 Discrete and Continuous Dynamical Systems. Series S
13 Nonlinear Analysis. Theory, Methods & Applications
12 SIAM Journal on Numerical Analysis
12 Journal of Nonlinear Science
11 Communications in Mathematical Physics
11 SIAM Journal on Applied Mathematics
11 Journal of Applied Analysis and Computation
10 Japan Journal of Industrial and Applied Mathematics
10 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
10 Communications in Partial Differential Equations
9 Communications in Nonlinear Science and Numerical Simulation
9 Boundary Value Problems
8 Mathematics of Computation
8 Annali di Matematica Pura ed Applicata. Serie Quarta
8 Stochastic Analysis and Applications
8 Applied Numerical Mathematics
8 Electronic Journal of Differential Equations (EJDE)
8 Acta Mathematica Sinica. English Series
8 Journal of Evolution Equations
8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
8 AIMS Mathematics
7 Journal of Statistical Physics
7 Mathematical Methods in the Applied Sciences
7 Bulletin of Mathematical Biology
7 European Journal of Applied Mathematics
7 NoDEA. Nonlinear Differential Equations and Applications
7 Differential Equations
7 Electronic Research Archive
6 Rocky Mountain Journal of Mathematics
6 Discrete Dynamics in Nature and Society
6 Qualitative Theory of Dynamical Systems
6 Science China. Mathematics
5 Computer Methods in Applied Mechanics and Engineering
5 Applied Mathematics and Optimization
5 Mathematische Annalen
5 Numerische Mathematik
5 Journal of the European Mathematical Society (JEMS)
5 Dynamical Systems
5 International Journal of Biomathematics
5 Molecular Based Mathematical Biology
4 Advances in Mathematics
4 Acta Mathematicae Applicatae Sinica. English Series
4 Asymptotic Analysis
4 Journal of Inequalities and Applications
4 Journal of Applied Mathematics
4 Comptes Rendus. Mathématique. Académie des Sciences, Paris
4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
4 Mathematical Biosciences and Engineering
4 Frontiers of Mathematics in China
4 International Journal for Numerical Methods in Biomedical Engineering
4 Journal of Elliptic and Parabolic Equations
3 Israel Journal of Mathematics
3 Journal d’Analyse Mathématique
3 Chaos, Solitons and Fractals
3 Mathematische Zeitschrift
3 Memoirs of the American Mathematical Society
3 Quarterly of Applied Mathematics
3 Studies in Applied Mathematics
3 Applied Mathematics and Mechanics. (English Edition)
3 Acta Applicandae Mathematicae
3 Journal of Integral Equations and Applications
3 The Annals of Applied Probability
3 Numerical Algorithms
3 Stochastic Processes and their Applications
3 Computational and Applied Mathematics
...and 177 more Serials
all top 5

Cited in 39 Fields

1,324 Partial differential equations (35-XX)
519 Dynamical systems and ergodic theory (37-XX)
320 Biology and other natural sciences (92-XX)
300 Ordinary differential equations (34-XX)
244 Probability theory and stochastic processes (60-XX)
181 Numerical analysis (65-XX)
154 Integral equations (45-XX)
140 Fluid mechanics (76-XX)
106 Operator theory (47-XX)
95 Statistical mechanics, structure of matter (82-XX)
73 Mechanics of deformable solids (74-XX)
50 Classical thermodynamics, heat transfer (80-XX)
48 Calculus of variations and optimal control; optimization (49-XX)
36 Global analysis, analysis on manifolds (58-XX)
31 Difference and functional equations (39-XX)
27 Real functions (26-XX)
23 Optics, electromagnetic theory (78-XX)
21 Functional analysis (46-XX)
18 Differential geometry (53-XX)
12 Mechanics of particles and systems (70-XX)
9 Systems theory; control (93-XX)
7 Approximations and expansions (41-XX)
7 Quantum theory (81-XX)
7 Information and communication theory, circuits (94-XX)
4 Linear and multilinear algebra; matrix theory (15-XX)
4 Computer science (68-XX)
4 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
3 Integral transforms, operational calculus (44-XX)
3 Operations research, mathematical programming (90-XX)
2 Measure and integration (28-XX)
2 Harmonic analysis on Euclidean spaces (42-XX)
2 Algebraic topology (55-XX)
2 Manifolds and cell complexes (57-XX)
2 Geophysics (86-XX)
1 General and overarching topics; collections (00-XX)
1 Combinatorics (05-XX)
1 Number theory (11-XX)
1 Field theory and polynomials (12-XX)
1 Potential theory (31-XX)

Citations by Year

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