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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
External Links: MGP · Wikidata
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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

101 Publications have been cited 3,538 times in 2,189 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
321
1997
Random attractors for stochastic reaction-diffusion equations on unbounded domains. Zbl 1155.35112
Bates, Peter W.; Lu, Kening; Wang, Bixiang
273
2009
Attractors for stochastic lattice dynamical systems. Zbl 1105.60041
Bates, Peter W.; Lisei, Hannelore; Lu, Kening
224
2006
Attractors for lattice dynamical systems. Zbl 1091.37515
Bates, Peter W.; Lu, Kening; Wang, Bixiang
178
2001
Convergence of the Cahn-Hilliard equation to the Hele-Shaw model. Zbl 0828.35105
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu
150
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
133
2007
A discrete convolution model for phase transitions. Zbl 0956.74037
Bates, Peter W.; Chmaj, Adam
127
1999
An integrodifferential model for phase transitions: stationary solutions in higher space dimensions. Zbl 0958.82015
Bates, Peter W.; Chmaj, Adam
109
1999
On some nonlocal evolution equations arising in materials science. Zbl 1101.35073
Bates, Peter W.
107
2006
Attractors of non-autonomous stochastic lattice systems in weighted spaces. Zbl 1364.34113
Bates, Peter W.; Lu, Kening; Wang, Bixiang
105
2014
Periodic traveling waves and locating oscillating patterns in multidimensional domains. Zbl 0929.35067
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu
99
1999
Traveling waves of bistable dynamics on a lattice. Zbl 1050.37041
Bates, Peter W.; Chen, Xinfu; Chmaj, Adam J. J.
98
2003
Slow motion for the Cahn-Hilliard equation in one space dimension. Zbl 0753.35042
Alikakos, Nicholas; Bates, Peter W.; Fusco, Giorgio
95
1991
Existence and persistence of invariant manifolds for semiflows in Banach space. Zbl 1023.37013
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
85
1998
The dynamics of nucleation for the Cahn-Hilliard equation. Zbl 0788.35061
Bates, Peter W.; Fife, Paul C.
78
1993
The Neumann boundary problem for a nonlocal Cahn-Hilliard equation. Zbl 1081.45004
Bates, Peter W.; Han, Jianlong
68
2005
Invariant manifolds for semilinear partial differential equations. Zbl 0674.58024
Bates, Peter W.; Jones, Christopher K. R. T.
64
1989
Dynamics of the 3-D fractional complex Ginzburg-Landau equation. Zbl 1328.35279
Lu, Hong; Bates, Peter W.; Lü, Shujuan; Zhang, Mingji
55
2015
Equilibria with many nuclei for the Cahn-Hilliard equation. Zbl 0990.35016
Bates, Peter W.; Fusco, Giorgio
47
2000
Approximately invariant manifolds and global dynamics of spike states. Zbl 1157.37013
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
47
2008
Numerical analysis for a nonlocal Allen-Cahn equation. Zbl 1165.65051
Bates, Peter W.; Brown, Sarah; Han, Jianlong
45
2009
Asymptotic behavior of stochastic fractional power dissipative equations on \(\mathbb{R}^n\). Zbl 1337.37062
Lu, Hong; Bates, Peter W.; Xin, Jie; Zhang, Mingji
44
2015
The Dirichlet boundary problem for a nonlocal Cahn-Hilliard equation. Zbl 1108.45004
Bates, Peter W.; Han, Jianlong
43
2005
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
43
1999
Existence and instability of spike layer solutions to singular perturbation problems. Zbl 1010.47036
Bates, Peter W.; Shi, Junping
37
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.
37
1990
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
36
2015
Inertial manifolds and inertial sets for the phase-field equations. Zbl 0758.35040
Bates, Peter W.; Zheng, Songmu
35
1992
Metastable patterns for the Cahn-Hilliard equation. I. Zbl 0805.35046
Bates, Peter W.; Xun, Jianping
35
1994
Invariant foliations near normally hyperbolic invariant manifolds for semiflows. Zbl 0964.37018
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
34
2000
Metastable patterns for the Cahn-Hilliard equation. II: Layer dynamics and slow invariant manifold. Zbl 0821.35074
Bates, Peter W.; Xun, Jianping
33
1995
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
33
2009
Spectral analysis and multidimensional stability of traveling waves for nonlocal Allen–Cahn equation. Zbl 1121.35322
Bates, Peter W.; Chen, Fengxin
33
2002
Spectral analysis of traveling waves for nonlocal evolution equations. Zbl 1134.35060
Bates, Peter W.; Chen, Fengxin
28
2006
Persistence of overflowing manifolds for semiflow. Zbl 0947.37009
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
27
1999
Periodic traveling waves for a nonlocal integro-differential model. Zbl 0924.35060
Bates, Peter; Chen, Fengxin
24
1999
Heteroclinic solutions of a van der Waals model with infinite nonlocal interactions. Zbl 1086.49008
Bates, Peter W.; Chen, Xinfu; Chmaj, Adam J. J.
24
2005
On the singular limit in a phase field model of phase transitions. Zbl 0696.35060
Alikakos, Nicholas D.; Bates, Peter W.
22
1988
Nucleation of instability of the Meissner state of 3-dimensional superconductors. Zbl 1137.82024
Bates, Peter W.; Pan, Xing-Bin
21
2007
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.
19
2016
Tempered random attractors for parabolic equations in weighted spaces. Zbl 1288.35097
Bates, Peter W.; Lu, Kening; Wang, Bixiang
19
2013
On a nonlocal phase-field system. Zbl 1092.35010
Bates, Peter W.; Han, Jianlong; Zhao, Guangyu
18
2006
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
Blow up for a diffusion-advection equation. Zbl 0707.35018
Alikakos, Nicholas D.; Bates, Peter W.; Grant, Christopher P.
17
1989
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
17
2017
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
16
1993
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
16
2017
Normally hyperbolic invariant manifolds for random dynamical systems. I: Persistence. Zbl 1291.37093
Li, Ji; Lu, Kening; Bates, Peter
15
2013
A Hartman-Grobman theorem for the Cahn-Hilliard and phase-field equations. Zbl 0795.35052
Bates, Peter W.; Lu, Kening
14
1994
Traveling pulses for the Klein-Gordon equation on a lattice or continuum with long-range interaction. Zbl 1119.34034
Bates, Peter W.; Zhang, Chunlei
12
2006
Invariant foliations for random dynamical systems. Zbl 1351.37215
Li, Ji; Lu, Kening; Bates, Peter W.
12
2014
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
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
11
2021
Global dynamics of boundary droplets. Zbl 1315.37049
Bates, Peter W.; Jin, Jiayin
10
2014
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
10
2019
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
Erratum: Nucleation of instability of the Meissner state of 3-dimensional superconductors. Zbl 1151.82439
Bates, Peter; Pan, Xing-Bin
9
2008
Containment for weakly coupled parabolic systems. Zbl 0581.35036
Bates, P. W.
9
1985
Multiphase solutions to the vector Allen-Cahn equation: crystalline and other complex symmetric structures. Zbl 1375.35538
Bates, Peter W.; Fusco, Giorgio; Smyrnelis, Panayotis
9
2017
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
9
2021
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
Mullins-Sekerka motion of small droplets on a fixed boundary. Zbl 0984.35013
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu; Fusco, Giorgio
7
2000
Global existence and uniqueness of solutions to a nonlocal phase-field system. Zbl 0938.35035
Bates, Peter W.; Chen, Fengxin; Wang, Junping
7
1997
Geometric singular perturbation theory with real noise. Zbl 1332.34099
Li, Ji; Lu, Kening; Bates, Peter W.
7
2015
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
Bifurcation and stability of periodic traveling waves for a reaction- diffusion system. Zbl 0494.35056
Barrow, David L.; Bates, Peter W.
6
1983
Transition layer solutions of a higher order equation in an infinite tube. Zbl 0904.35019
Bates, Peter W.; Ren, Xiaofeng
6
1996
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
6
2020
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
Entire solutions with six-fold junctions to elliptic gradient systems with triangle symmetry. Zbl 1277.35157
Bates, Peter; Fusco, Giorgio; Smyrnelis, Panayotis
5
2013
Invariant foliations of overflowing manifolds for semiflows in Banach space. Zbl 0971.37015
Bates, Peter; Lu, Kening; Zeng, Chongchun
4
1999
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
Heteroclinic orbits for a higher order phase transition problem. Zbl 0873.35099
Bates, Peter W.; Ren, Xiaofeng
4
1997
Hilbert space methods for nonlinear elliptic equations. Zbl 0365.34072
Bates, Peter W.
4
1979
Gradient dynamics: motion near a manifold of quasi-equilibria. Zbl 1409.37076
Bates, Peter; Fusco, Giorgio; Karali, Georgia
4
2018
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
Persistence of \(C^k\) normally hyperbolic invariant manifolds for infinite dimensional dynamical systems. Zbl 1288.37028
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
3
2001
A saddle-point theorem. Zbl 0599.34039
Bates, Peter W.; Ekeland, Ivar
3
1980
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
Growth regulation and the insulin signaling pathway. Zbl 1263.92013
Bates, Peter W.; Liang, Yu; Shingleton, Alexander W.
3
2013
Traveling wave solutions for a nonlocal phase-field system. Zbl 1010.35107
Bates, Peter W.; Chen, Fengxin
3
2002
Singular fold with real noise. Zbl 1366.37120
Zhang, Mingji; Li, Ji; Bates, Peter W.
3
2016
Reduction theorems for a class of semilinear equations at resonance. Zbl 0496.47052
Bates, Peter W.
2
1982
A numerical scheme for the two phase Mullins-Sekerka problem. Zbl 0823.65138
Bates, Peter W.; Chen, Xinfu; Deng, Xinyu
2
1995
A numerical scheme for the Mullins-Sekerka evolution in three space dimensions. Zbl 0960.65113
Bates, Peter W.; Brown, Sarah
2
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
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
Coarsening and nucleation in the Cahn-Hilliard equation. Zbl 0841.35130
Bates, P. W.
2
1993
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
Bifurcation of periodic travelling waves for a reaction-diffuion system. Zbl 0508.35044
Barrow, D. L.; Bates, P. W.
1
1982
Travelling waves in radially symmetric parabolic systems. Zbl 0567.35045
Bates, Peter W.
1
1985
Necessary and sufficient conditions for existence of solutions to equations with noninvertible linear part. Zbl 0473.47048
Bates, Peter W.; Castro, Alfonso
1
1981
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
Neck-linker tension and the locomotion of kinesin along microtubules. Zbl 1216.92039
Bates, Peter W.; Jia, Zhiyuan
1
2010
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
11
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
9
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
6
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
10
2019
Gradient dynamics: motion near a manifold of quasi-equilibria. Zbl 1409.37076
Bates, Peter; Fusco, Giorgio; Karali, Georgia
4
2018
The spectral collocation method for efficiently solving PDEs with fractional Laplacian. Zbl 1395.65106
Lu, Hong; Bates, Peter W.; Chen, Wenping; Zhang, Mingji
1
2018
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
17
2017
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
16
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
9
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.
19
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
55
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
44
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
36
2015
Geometric singular perturbation theory with real noise. Zbl 1332.34099
Li, Ji; Lu, Kening; Bates, Peter W.
7
2015
Attractors of non-autonomous stochastic lattice systems in weighted spaces. Zbl 1364.34113
Bates, Peter W.; Lu, Kening; Wang, Bixiang
105
2014
Invariant foliations for random dynamical systems. Zbl 1351.37215
Li, Ji; Lu, Kening; Bates, Peter W.
12
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
15
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
273
2009
Numerical analysis for a nonlocal Allen-Cahn equation. Zbl 1165.65051
Bates, Peter W.; Brown, Sarah; Han, Jianlong
45
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
33
2009
Approximately invariant manifolds and global dynamics of spike states. Zbl 1157.37013
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
47
2008
Erratum: Nucleation of instability of the Meissner state of 3-dimensional superconductors. Zbl 1151.82439
Bates, Peter; Pan, Xing-Bin
9
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
133
2007
Nucleation of instability of the Meissner state of 3-dimensional superconductors. Zbl 1137.82024
Bates, Peter W.; Pan, Xing-Bin
21
2007
Attractors for stochastic lattice dynamical systems. Zbl 1105.60041
Bates, Peter W.; Lisei, Hannelore; Lu, Kening
224
2006
On some nonlocal evolution equations arising in materials science. Zbl 1101.35073
Bates, Peter W.
107
2006
Spectral analysis of traveling waves for nonlocal evolution equations. Zbl 1134.35060
Bates, Peter W.; Chen, Fengxin
28
2006
On a nonlocal phase-field system. Zbl 1092.35010
Bates, Peter W.; Han, Jianlong; Zhao, Guangyu
18
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
12
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
68
2005
The Dirichlet boundary problem for a nonlocal Cahn-Hilliard equation. Zbl 1108.45004
Bates, Peter W.; Han, Jianlong
43
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.
24
2005
Traveling waves of bistable dynamics on a lattice. Zbl 1050.37041
Bates, Peter W.; Chen, Xinfu; Chmaj, Adam J. J.
98
2003
Existence and instability of spike layer solutions to singular perturbation problems. Zbl 1010.47036
Bates, Peter W.; Shi, Junping
37
2002
Spectral analysis and multidimensional stability of traveling waves for nonlocal Allen–Cahn equation. Zbl 1121.35322
Bates, Peter W.; Chen, Fengxin
33
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
178
2001
Persistence of \(C^k\) normally hyperbolic invariant manifolds for infinite dimensional dynamical systems. Zbl 1288.37028
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
3
2001
Equilibria with many nuclei for the Cahn-Hilliard equation. Zbl 0990.35016
Bates, Peter W.; Fusco, Giorgio
47
2000
Invariant foliations near normally hyperbolic invariant manifolds for semiflows. Zbl 0964.37018
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
34
2000
Mullins-Sekerka motion of small droplets on a fixed boundary. Zbl 0984.35013
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu; Fusco, Giorgio
7
2000
A numerical scheme for the Mullins-Sekerka evolution in three space dimensions. Zbl 0960.65113
Bates, Peter W.; Brown, Sarah
2
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 discrete convolution model for phase transitions. Zbl 0956.74037
Bates, Peter W.; Chmaj, Adam
127
1999
An integrodifferential model for phase transitions: stationary solutions in higher space dimensions. Zbl 0958.82015
Bates, Peter W.; Chmaj, Adam
109
1999
Periodic traveling waves and locating oscillating patterns in multidimensional domains. Zbl 0929.35067
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu
99
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
43
1999
Persistence of overflowing manifolds for semiflow. Zbl 0947.37009
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
27
1999
Periodic traveling waves for a nonlocal integro-differential model. Zbl 0924.35060
Bates, Peter; Chen, Fengxin
24
1999
Invariant foliations of overflowing manifolds for semiflows in Banach space. Zbl 0971.37015
Bates, Peter; Lu, Kening; Zeng, Chongchun
4
1999
Existence and persistence of invariant manifolds for semiflows in Banach space. Zbl 1023.37013
Bates, Peter W.; Lu, Kening; Zeng, Chongchun
85
1998
Traveling waves in a convolution model for phase transitions. Zbl 0889.45012
Bates, Peter W.; Fife, Paul C.; Ren, Xiaofeng; Wang, Xuefeng
321
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
33
1995
A numerical scheme for the two phase Mullins-Sekerka problem. Zbl 0823.65138
Bates, Peter W.; Chen, Xinfu; Deng, Xinyu
2
1995
Convergence of the Cahn-Hilliard equation to the Hele-Shaw model. Zbl 0828.35105
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu
150
1994
Metastable patterns for the Cahn-Hilliard equation. I. Zbl 0805.35046
Bates, Peter W.; Xun, Jianping
35
1994
A Hartman-Grobman theorem for the Cahn-Hilliard and phase-field equations. Zbl 0795.35052
Bates, Peter W.; Lu, Kening
14
1994
The dynamics of nucleation for the Cahn-Hilliard equation. Zbl 0788.35061
Bates, Peter W.; Fife, Paul C.
78
1993
Solutions to the nonautonomous bistable equation with specified Morse index. I: Existence. Zbl 0788.34012
Alikakos, Nicholas D.; Bates, Peter W.; Fusco, Giorgio
16
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
95
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.
37
1990
Invariant manifolds for semilinear partial differential equations. Zbl 0674.58024
Bates, Peter W.; Jones, Christopher K. R. T.
64
1989
Blow up for a diffusion-advection equation. Zbl 0707.35018
Alikakos, Nicholas D.; Bates, Peter W.; Grant, Christopher P.
17
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.
22
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
3
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
...and 1 more Documents
all top 5

Cited by 2,122 Authors

76 Wang, Bixiang
65 Li, Wan-Tong
55 Zhou, Shengfan
48 Li, Yangrong
41 Bates, Peter W.
32 Shen, Wenxian
31 Lu, Kening
29 Caraballo Garrido, Tomás
29 Rossi, Julio Daniel
29 Wei, Juncheng
28 Wang, Renhai
27 Kloeden, Peter Eris
25 Gu, Anhui
25 Han, Xiaoying
24 Shu, Ji
23 Li, Dingshi
23 Sun, Jianwen
23 Zhao, Caidi
22 Zhang, Mingji
21 Grasselli, Maurizio
21 Hupkes, Hermen Jan
21 Ruan, Shigui
19 Chen, Zhang
18 Du, Qiang
18 Yang, Feiying
17 Fusco, Giorgio
17 Wang, Zhi Cheng
16 Coville, Jerome
16 Pan, Xingbin
16 Shi, Junping
15 Chen, Xinfu
15 de la Llave, Rafael
15 Lin, Guo
15 Wang, Xiaohu
15 Wang, Zhaojuan
15 Xu, Zhaoquan
14 Abdallah, Ahmed Y.
14 Alikakos, Nicholas D.
14 Du, Yihong
14 Yuan, Rong
14 Zhao, Wenqiang
13 Abels, Helmut
13 Guo, Shangjiang
13 Karali, Georgia D.
13 Valero, José
13 Wang, Jiabing
13 Wei, Guowei
13 Wu, Shiliang
13 Zhang, Guobao
12 Gal, Ciprian Gheorghe Sorin
12 Shi, Lin
12 Van Vleck, Erik S.
12 Yang, Shuang
12 Zhao, Shan
11 Miranville, Alain M.
11 Pan, Shuxia
11 Strani, Marta
11 Yang, Jun
11 Zhao, Xiao-Qiang
10 Cortázar, Carmen
10 Hsu, Cheng-Hsiung
10 Kühn, Christian
10 Lu, Hong
10 Morillas, Francisco G.
10 Nefedov, Nikolaĭ Nikolaevich
10 Wang, Mingxin
10 Wang, Yejuan
10 Weng, Peixuan
10 Winter, Matthias
10 Wolanski, Noemi I.
10 Yang, Xiaofeng
10 Zhang, Jian
9 Elgueta, Manuel
9 Frigeri, Sergio
9 Li, Fuzhi
9 Li, Ji
9 Promislow, Keith Steven
9 Shen, Jun
9 Shen, Zhongwei
9 Souplet, Philippe
9 Sprekels, Jürgen
9 Zhao, Min
8 Cheng, Cuiping
8 D’Elia, Marta
8 Ei, Shin-Ichiro
8 Folino, Raffaele
8 Garcke, Harald
8 Gunzburger, Max D.
8 Guo, Chunxiao
8 Kowalczyk, Michał
8 Li, Xiaojun
8 Novick-Cohen, Amy
8 Sheng, WeiJie
8 Sourdis, Christos
8 Wang, Cheng
8 Zeng, Chongchun
8 Zhao, Guangyu
8 Zhao, Huaizhong
7 Bhowmik, Samir Kumar
7 Blömker, Dirk
...and 2,022 more Authors
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Cited in 305 Serials

223 Journal of Differential Equations
100 Discrete and Continuous Dynamical Systems. Series B
87 Journal of Mathematical Analysis and Applications
85 Journal of Dynamics and Differential Equations
70 Discrete and Continuous Dynamical Systems
67 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
46 Journal of Mathematical Physics
41 Communications on Pure and Applied Analysis
37 Applied Mathematics and Computation
34 Physica D
33 Journal of Computational Physics
32 Calculus of Variations and Partial Differential Equations
31 Archive for Rational Mechanics and Analysis
30 Nonlinearity
28 Nonlinear Analysis. Real World Applications
28 Discrete and Continuous Dynamical Systems. Series S
27 Proceedings of the American Mathematical Society
27 SIAM Journal on Mathematical Analysis
26 Computers & Mathematics with Applications
26 Transactions of the American Mathematical Society
25 ZAMP. Zeitschrift für angewandte Mathematik und Physik
24 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
24 Stochastics and Dynamics
23 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
22 Journal of Computational and Applied Mathematics
22 Applied Mathematics Letters
22 Journal of Scientific Computing
20 Abstract and Applied Analysis
18 Journal de Mathématiques Pures et Appliquées. Neuvième Série
18 Communications in Nonlinear Science and Numerical Simulation
18 SIAM Journal on Applied Dynamical Systems
16 Journal of Difference Equations and Applications
15 Applicable Analysis
15 Communications in Mathematical Physics
15 Journal of Mathematical Biology
15 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
14 Mathematical Methods in the Applied Sciences
14 Journal of Functional Analysis
14 SIAM Journal on Numerical Analysis
14 Journal of Nonlinear Science
14 Qualitative Theory of Dynamical Systems
13 SIAM Journal on Applied Mathematics
13 Advances in Difference Equations
13 Nonlinear Analysis. Theory, Methods & Applications
11 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
11 Communications in Partial Differential Equations
11 Journal of Applied Analysis and Computation
10 Stochastic Analysis and Applications
10 European Journal of Applied Mathematics
10 Japan Journal of Industrial and Applied Mathematics
10 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
9 Mathematics of Computation
9 Electronic Journal of Differential Equations (EJDE)
9 Journal of Evolution Equations
9 Boundary Value Problems
9 Electronic Research Archive
8 Journal of Statistical Physics
8 Bulletin of Mathematical Biology
8 Annali di Matematica Pura ed Applicata. Serie Quarta
8 Applied Numerical Mathematics
8 NoDEA. Nonlinear Differential Equations and Applications
8 Acta Mathematica Sinica. English Series
8 Science China. Mathematics
8 AIMS Mathematics
7 Computer Methods in Applied Mechanics and Engineering
7 Applied Mathematics and Optimization
7 Mathematische Annalen
7 Asymptotic Analysis
7 Discrete Dynamics in Nature and Society
7 Differential Equations
7 Dynamical Systems
7 International Journal of Biomathematics
6 Rocky Mountain Journal of Mathematics
6 Numerical Methods for Partial Differential Equations
6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
5 Journal d’Analyse Mathématique
5 Advances in Mathematics
5 Memoirs of the American Mathematical Society
5 Numerische Mathematik
5 Acta Applicandae Mathematicae
5 Journal of the European Mathematical Society (JEMS)
5 Analysis and Applications (Singapore)
5 Advances in Nonlinear Analysis
5 Molecular Based Mathematical Biology
4 Acta Mathematicae Applicatae Sinica. English Series
4 The Journal of Geometric Analysis
4 Bulletin des Sciences Mathématiques
4 Advances in Differential Equations
4 Journal of Inequalities and Applications
4 Interfaces and Free Boundaries
4 Communications in Contemporary Mathematics
4 Annales Henri Poincaré
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 Communications in Computational Physics
4 Banach Journal of Mathematical Analysis
4 International Journal for Numerical Methods in Biomedical Engineering
...and 205 more Serials
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Cited in 43 Fields

1,568 Partial differential equations (35-XX)
624 Dynamical systems and ergodic theory (37-XX)
378 Biology and other natural sciences (92-XX)
336 Ordinary differential equations (34-XX)
310 Probability theory and stochastic processes (60-XX)
222 Numerical analysis (65-XX)
186 Integral equations (45-XX)
168 Fluid mechanics (76-XX)
123 Operator theory (47-XX)
103 Statistical mechanics, structure of matter (82-XX)
79 Mechanics of deformable solids (74-XX)
60 Calculus of variations and optimal control; optimization (49-XX)
53 Classical thermodynamics, heat transfer (80-XX)
39 Global analysis, analysis on manifolds (58-XX)
37 Difference and functional equations (39-XX)
34 Real functions (26-XX)
31 Optics, electromagnetic theory (78-XX)
25 Differential geometry (53-XX)
22 Functional analysis (46-XX)
17 Mechanics of particles and systems (70-XX)
12 Systems theory; control (93-XX)
10 Approximations and expansions (41-XX)
9 Information and communication theory, circuits (94-XX)
8 Quantum theory (81-XX)
6 Computer science (68-XX)
5 Linear and multilinear algebra; matrix theory (15-XX)
4 Harmonic analysis on Euclidean spaces (42-XX)
4 Operations research, mathematical programming (90-XX)
4 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
3 Combinatorics (05-XX)
3 Measure and integration (28-XX)
3 Integral transforms, operational calculus (44-XX)
3 Geophysics (86-XX)
2 General and overarching topics; collections (00-XX)
2 Number theory (11-XX)
2 Potential theory (31-XX)
2 Algebraic topology (55-XX)
2 Manifolds and cell complexes (57-XX)
1 Field theory and polynomials (12-XX)
1 Group theory and generalizations (20-XX)
1 Abstract harmonic analysis (43-XX)
1 Geometry (51-XX)
1 Statistics (62-XX)

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