Edit Profile (opens in new tab) Bates, Peter W. Co-Author Distance Author ID: bates.peter-w Published as: Bates, Peter W.; Bates, P. W.; Bates, Peter more...less External Links: MGP · Wikidata Documents Indexed: 113 Publications since 1975, including 1 Book 3 Contributions as Editor Co-Authors: 65 Co-Authors with 105 Joint Publications 1,729 Co-Co-Authors all top 5 Co-Authors 11 single-authored 21 Lu, Kening 14 Alikakos, Nicholas D. 11 Zhang, Mingji 10 Fusco, Giorgio 10 Zeng, Chongchun 8 Chen, Xinfu 7 Chen, Fengxin 7 Lu, Hong 6 Fife, Paul C. 5 Chmaj, Adam J. J. 5 Jones, Christopher K. R. T. 4 Han, Jianlong 4 Li, Ji 4 Wang, Bixiang 3 Barrow, David L. 3 Gustafson, Grant B. 3 Pan, Xingbin 3 Ren, Xiaofeng 2 Brown, Sarah E. 2 Castro, Alfonso 2 Gardner, Robert A. 2 Jin, Jiayin 2 Karali, Georgia D. 2 Lu, Shujuan 2 Shi, Junping 2 Smyrnelis, Panayotis 2 Wen, Zhenshu 2 Xun, Jianping 2 Zhao, Guangyu 1 Aitbayev, Rakhim 1 Antonopoulou, Dimitra C. 1 Blömker, Dirk 1 Brown, Kenneth J. 1 Cahn, John W. 1 Chen, Jianing 1 Chen, Wenping 1 Chen, Zhan 1 Chow, Shui-Nee 1 Dancer, Edward Norman 1 Deng, Xinyu 1 Ekeland, Ivar 1 Grant, Christopher P. 1 Hilhorst, Danielle 1 Jia, Yusheng 1 Jia, Zhiyuan 1 Liang, Yu 1 Lin, Guojian 1 Lisei, Hannelore 1 Liu, Weishi 1 Matano, Hiroshi 1 Morita, Yoshihisa 1 Shingleton, Alexander W. 1 Sun, Yuhui 1 Tanoğlu, Gamze B. 1 Wang, Junping 1 Wang, Ping 1 Wang, Xuefeng 1 Ward, James Robert jun. 1 Wei, Guowei 1 Xin, Jie 1 Xu, Daoyi 1 Zhang, Chunlei 1 Zhang, Lijun 1 Zhao, Shan 1 Zheng, Songmu all top 5 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 all top 5 Fields 75 Partial differential equations (35-XX) 34 Ordinary differential equations (34-XX) 33 Dynamical systems and ergodic theory (37-XX) 15 Biology and other natural sciences (92-XX) 11 Operator theory (47-XX) 11 Numerical analysis (65-XX) 11 Statistical mechanics, structure of matter (82-XX) 9 Classical thermodynamics, heat transfer (80-XX) 8 Integral equations (45-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Fluid mechanics (76-XX) 6 Mechanics of deformable solids (74-XX) 4 Probability theory and stochastic processes (60-XX) 3 General and overarching topics; collections (00-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Optics, electromagnetic theory (78-XX) 2 Differential geometry (53-XX) 1 History and biography (01-XX) 1 Functional analysis (46-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX) Publications by Year all cited Publications top 5 cited Publications 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 cited Publications top 5 cited Publications 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 all top 5 Cited in 305 Serials 223 Journal of Differential Equations 100 Discrete and Continuous Dynamical Systems. 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