P. Bates

发表

International Journal of C 2009 Institute for Scientific Numerical Analysis and Modeling Computing and Information Numerical Analysis for a Nonlocal Allen-cahn Equation

P. Bates, Sarah M. Brown, Jianlong Han, 2022 .

Traveling Waves in a Convolution Model for Phase Transitions

P. Bates, P. Fife, X. Ren, 1997 .

Slow motion for the Cahn-Hilliard equation in one space dimension

Peter W. Bates, Giorgio Fusco, Nicholas D. Alikakos, 1991 .

ATTRACTORS FOR STOCHASTIC LATTICE DYNAMICAL SYSTEMS

P. Bates, K. Lu, H. Lisei, 2006 .

Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space

Peter W. Bates, Kening Lu, Chongchun Zeng, 1998 .

Geometric singular perturbation theory with real noise

P. Bates, K. Lu, Ji Li, 2015 .

Encyclopaedia of Mathematics, Supplement III

Konrad Engel, Willy Govaerts, Francisco Marcellán, 2002 .

Convergence of the Cahn-Hilliard equation to the Hele-Shaw model

Peter W. Bates, Xinfu Chen, Nicholas D. Alikakos, 1994 .

The Dirichlet boundary problem for a nonlocal Cahn–Hilliard equation

Peter W. Bates, P. Bates, Jianlong Han, 2005 .

Geometric and potential driving formation and evolution of biomolecular surfaces

Shan Zhao, Guo-Wei Wei, Zhan Chen, 2009, Journal of mathematical biology.

Global dynamics of boundary droplets

Peter W. Bates, P. Bates, Jiayin Jin, 2013 .

Spectral comparison principles for the Cahn-Hilliard and phase-field equations, and time scales for coarsening

Peter W. Bates, P. Bates, P. Fife, 1990 .

Persistence of Overflowing Manifolds for Semiflow

Peter W. Bates, Kening Lu, Chongchun Zeng, 1999 .

Attractors of non-autonomous stochastic lattice systems in weighted spaces

P. Bates, K. Lu, Bixiang Wang, 2014 .

Tempered random attractors for parabolic equations in weighted spaces

P. Bates, K. Lu, Bixiang Wang, 2013 .

Equilibria with Many Nuclei for the Cahn–Hilliard Equation

P. Bates, G. Fusco, 2000 .

Ion size and valence effects on ionic flows via Poisson-Nernst-Planck models

P. Bates, Hong Lu, Weishi Liu, 2017 .

Metastable Patterns for the Cahn-Hilliard Equation: Part II. Layer Dynamics and Slow Invariant Manifold

Peter W. Bates, P. Bates, J. P. Xun, 1995 .

Nucleation of Instability of the Meissner State of 3-Dimensional Superconductors

P. Bates, Xingbin Pan, 2007 .

A VARIATIONAL APPROACH TO SOLVING SEMILINEAR EQUATIONS AT RESONANCE

P. Bates, 1982 .

Singular fold with real noise

P. Bates, Mingji Zhang, Ji Li, 2016 .

Convergence to equilibrium in a reaction-diffusion system

K. J. Brown, P. Bates, 1984 .

A numerical scheme for the two phase Mullins-Sekerka problem

P. Bates, Xinfu Chen, Xin Deng, 1995 .

Phase field models for hypercooled solidification

P. Bates, P. Fife, R. Gardner, 1997 .

Random attractors for stochastic reaction–diffusion equations on unbounded domains

Peter W. Bates, Bixiang Wang, Kening Lu, 2009 .

Invariant foliations for random dynamical systems

P. Bates, K. Lu, Ji Li, 2014 .

A Discrete Convolution Model¶for Phase Transitions

Peter W. Bates, Adam J. J. Chmaj, P. Bates, 1999 .

Developmental model of static allometry in holometabolous insects

P. Bates, C. Mirth, A. Shingleton, 2008, Proceedings of the Royal Society B: Biological Sciences.

Invariant Manifolds for Semilinear Partial Differential Equations

Peter W. Bates, Christopher K. R. T. Jones, P. Bates, 1989 .

Small Permanent Charge Effects on Individual Fluxes via Poisson–Nernst–Planck Models with Multiple Cations

Peter W. Bates, Mingji Zhang, Zhenshu Wen, 2021, Journal of Nonlinear Science.

Effects on I–V relations from small permanent charge and channel geometry via classical Poisson–Nernst–Planck equations with multiple cations

P. Bates, Mingji Zhang, Zhenshu Wen, 2021, Nonlinearity.

Dynamics of the 3-D fractional complex Ginzburg-Landau equation

P. Bates, Shujuan Lü, Hong Lu, 2015 .

Variational approach for nonpolar solvation analysis.

Shan Zhao, Nathan A. Baker, Jaehun Chun, 2012, The Journal of chemical physics.

Minimal molecular surfaces and their applications

Shan Zhao, Guo-Wei Wei, Peter W. Bates, 2008, J. Comput. Chem..

Motion of a Droplet for the Stochastic Mass-Conserving Allen-Cahn Equation

Peter W. Bates, D. C. Antonopoulou, Georgia D. Karali, 2016, SIAM J. Math. Anal..

Analysis of a corner layer problem in anisotropic interfaces

J. Cahn, P. Bates, P. Fife, 2005 .

Periodic traveling waves and locating oscillating patterns in multidimensional domains

Peter W. Bates, Xinfu Chen, Nicholas D. Alikakos, 1999 .

Multiphase Solutions to the Vector Allen–Cahn Equation: Crystalline and Other Complex Symmetric Structures

P. Bates, G. Fusco, Panayotis Smyrnelis, 2014, 1411.4008.

Approximately invariant manifolds and global dynamics of spike states

Peter W. Bates, Kening Lu, Chongchun Zeng, 2008 .

Traveling Waves of Bistable Dynamics on a Lattice

Xinfu Chen, Peter W. Bates, Adam J. J. Chmaj, 2003, SIAM J. Math. Anal..

The minimal molecular surface

Shan Zhao, G. Wei, P. Bates, 2006, q-bio/0610038.

A Hartman-Grobman theorem for the Cahn-Hilliard and phase-field equations

Peter W. Bates, Kening Lu, P. Bates, 1994 .

Mathematical studies of Poisson-Nernst-Planck model for membrane channels: Finite ion size effects without electroneutrality boundary conditions

Peter W. Bates, Mingji Zhang, Rakhim Aitbayev, 2019, J. Comput. Appl. Math..

Invariant foliations near normally hyperbolic invariant manifolds for semiflows

Peter W. Bates, Kening Lu, Chongchun Zeng, 2000 .

Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal

Peter W. Bates, Guangyu Zhao, P. Bates, 2007 .

ON SOME NONLOCAL EVOLUTION EQUATIONS ARISING IN MATERIALS SCIENCE

Xinfu Chen, Adam J. J. Chmaj, Guangyu Zhao, 2008 .

Estimates for the eigenvalues of the Jordan product of Hermitian matrices

P. Bates, N. Alikakos, 1984 .

The Dynamics of Nucleation for the Cahn-Hilliard Equation

Peter W. Bates, Paul C. Fife, P. Bates, 1993, SIAM J. Appl. Math..

Inertial manifolds and inertial sets for the phase-field equations

P. Bates, Songmu Zheng, 1992 .

Entire Solutions with Six-fold Junctions to Elliptic Gradient Systems with Triangle Symmetry

P. Bates, Panayotis Smyrnelis, Giorgio Fuscoy, 2013 .

Spectral analysis and multidimensional stability of traveling waves for nonlocal Allen-Cahn equation

Peter W. Bates, Fengxin Chen, P. Bates, 2002 .

Hilbert space methods for nonlinear elliptic equations

P. Bates, 1979 .

Spectral analysis of traveling waves for nonlocal evolution equations

Peter W. Bates, Fengxin Chen, P. Bates, 2006, SIAM J. Math. Anal..

Attractors for Lattice Dynamical Systems

Peter W. Bates, Bixiang Wang, Kening Lu, 2001, Int. J. Bifurc. Chaos.

Dynamics of ionic flows via Poisson-Nernst-Planck systems with local hard-sphere potentials: Competition between cations.

P. Bates, Jianing Chen, Ming Ji Zhang, 2020, Mathematical biosciences and engineering : MBE.

Normally hyperbolic invariant manifolds for random dynamical systems: Part I - persistence

Peter W. Bates, Kening Lu, Ji Li, 2013 .

Global Dynamics of Particles Driven by a Nonlinear Reaction-Diffusion Equation (Far-From-Equilibrium Dynamics)

P. Bates, K. Lu, C. Zeng, 2012 .

The existence of travelling wave solutions of a generalized phase-field model

P. Bates, P. Fife, R. Gardner, 1997 .

Heteroclinic solutions of a van der Waals model with indefinite nonlocal interactions

Adam J. J. Chmaj, P. Bates, Xinfu Chen, 2005 .

An Integrodifferential Model for Phase Transitions: Stationary Solutions in Higher Space Dimensions

Peter W. Bates, Adam J. J. Chmaj, P. Bates, 1999 .

Existence and instability of spike layer solutions to singular perturbation problems

P. Bates, Junping Shi, 2002 .

Solutions to the Nonautonomous Bistable Equation with Specified Morse Index. Part I: Existence

P. Bates, N. Alikakos, G. Fusco, 1993 .

Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability

E. N. Dancer, P. Bates, Junping Shi, 1999, Advances in Differential Equations.

Individual Flux Study via Steady-State Poisson-Nernst-Planck Systems: Effects from Boundary Conditions

Peter W. Bates, Yusheng Jia, Guojian Lin, 2017, SIAM J. Appl. Dyn. Syst..

On a nonlocal phase-field system

Peter W. Bates, Guangyu Zhao, P. Bates, 2006 .

The Neumann boundary problem for a nonlocal Cahn–Hilliard equation

Peter W. Bates, P. Bates, Jianlong Han, 2005 .

Blow up for a diffusion-advection equation

Christopher P. Grant, P. Bates, N. Alikakos, 1989, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

Periodic traveling waves fora nonlocal integro-dierential model

P. Bates, Fengxin Chen, 1999 .

Asymptotic behavior of stochastic fractional power dissipative equations on Rn

P. Bates, J. Xin, Hong Lu, 2015 .

Metastable Patterns for the Cahn-Hilliard Equation, Part I

P. Bates, J. Xun, 1994 .

Simulation studies of self-organization of microtubules and molecular motors.

I. Aranson, P. Bates, D. Karpeev, 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

Growth regulation and the insulin signaling pathway

Peter W. Bates, Yu Liang, Alexander W. Shingleton, 2013, Networks Heterog. Media.

On the singular limit in a phase field model of phase transitions

P. Bates, N. Alikakos, 1988 .

Dynamics of the 3D fractional Ginzburg–Landau equation with multiplicative noise on an unbounded domain

P. Bates, Shujuan Lü, Hong Lu, 2016 .

Existence and uniqueness for a variational hyperbolic system without resonance

Peter W. Bates, Alfonso Castro, P. Bates, 1980 .

Solutions of nonlinear elliptic systems with meshed spectra

P. Bates, 1980 .

Motion of a droplet for the mass-conserving stochastic Allen-Cahn equation

P. Bates, D. Antonopoulou, G. Karali, 2015, 1501.05288.

Stabilization of solutions for a class of degenerate equations in divergence form in one space dimension

P. Bates, N. Alikakos, 1988 .

A N INVARIANCE PRINCIPLE FOR A CLASS OF MONOTONE SYSTEMS A N D APPLICATION TO DEGENERATE PARABOLIC EQUATIONS

P. Bates, 2008 .

Solutions to the Nonautonomous Bistable Equation with Specified Morse Index. Part I: Existence

P. Bates, N. Alikakos, G. Fusco, 1993 .

A SADDLE-POINT THEOREM

I. Ekeland, P. Bates, 1980 .

Invariant manifolds of interior multi-spike states for the Cahn-Hilliard equation in higher space dimensions

P. Bates, G. Fusco, Jiayin Jin, 2016 .

Giant vortex and the breakdown of pinning in a rotating Bose–Einstein condensate

P. Bates, Xinfu Chen, 2004 .

Green's function inequalities for two-point boundary value problems.

P. Bates, G. Gustafson, 1975 .

Maximization of Green’s Function over Classes of Multipoint Boundary Value Problems

P. Bates, G. Gustafson, 1976 .

Mullins-Sekerka motion of small droplets on a fixed boundary

P. Bates, N. Alikakos, G. Fusco, 2000 .