Peter W. Bates | Academic Influence

Peter W. Bates's AcademicInfluence.com Rankings

Peter W. Bates

Mathematics

#5888

World Rank

#8241

Historical Rank

Measure Theory

#3176

World Rank

#3761

Historical Rank

mathematics Degrees

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Mathematics

Peter W. Bates's Degrees

Bachelors Mathematics Stanford University

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Why Is Peter W. Bates Influential?

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According to Wikipedia, Peter W. Bates is a professor of mathematics at Michigan State University. Bates received his Ph.D. from the University of Utah in 1976. In 2012, Bates became a fellow of the American Mathematical Society.

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Peter W. Bates's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Traveling Waves in a Convolution Model for Phase Transitions (1997) (553)
Convergence of the Cahn-Hilliard equation to the Hele-Shaw model (1994) (385)
Random attractors for stochastic reaction–diffusion equations on unbounded domains (2009) (336)
Invariant Manifolds for Semilinear Partial Differential Equations (1989) (258)
ATTRACTORS FOR STOCHASTIC LATTICE DYNAMICAL SYSTEMS (2006) (253)
Slow motion for the Cahn-Hilliard equation in one space dimension (1991) (216)
Attractors for Lattice Dynamical Systems (2001) (211)
Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space (1998) (210)
A Discrete Convolution Model¶for Phase Transitions (1999) (208)
An Integrodifferential Model for Phase Transitions: Stationary Solutions in Higher Space Dimensions (1999) (202)
The Dynamics of Nucleation for the Cahn-Hilliard Equation (1993) (174)
Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal (2007) (171)
Traveling Waves of Bistable Dynamics on a Lattice (2003) (130)
ON SOME NONLOCAL EVOLUTION EQUATIONS ARISING IN MATERIALS SCIENCE (2008) (128)
Minimal molecular surfaces and their applications (2008) (126)
Periodic traveling waves and locating oscillating patterns in multidimensional domains (1999) (125)
The Neumann boundary problem for a nonlocal Cahn–Hilliard equation (2005) (114)
Equilibria with Many Nuclei for the Cahn–Hilliard Equation (2000) (114)
Attractors of non-autonomous stochastic lattice systems in weighted spaces (2014) (112)
Developmental model of static allometry in holometabolous insects (2008) (112)
Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability (1999) (109)
Spectral comparison principles for the Cahn-Hilliard and phase-field equations, and time scales for coarsening (1990) (90)
Approximately invariant manifolds and global dynamics of spike states (2008) (88)
Geometric and potential driving formation and evolution of biomolecular surfaces (2009) (85)
Metastable Patterns for the Cahn-Hilliard Equation, Part I (1994) (85)
Invariant foliations near normally hyperbolic invariant manifolds for semiflows (2000) (83)
Existence and instability of spike layer solutions to singular perturbation problems (2002) (79)
Metastable Patterns for the Cahn-Hilliard Equation: Part II. Layer Dynamics and Slow Invariant Manifold (1995) (78)
The Dirichlet boundary problem for a nonlocal Cahn–Hilliard equation (2005) (65)
Inertial manifolds and inertial sets for the phase-field equations (1992) (60)
Encyclopaedia of Mathematics, Supplement III (2002) (59)
Persistence of Overflowing Manifolds for Semiflow (1999) (58)
Dynamics of the 3-D fractional complex Ginzburg-Landau equation (2015) (54)
Numerical analysis for a nonlocal Allen-Cahn equation (2009) (54)
Variational approach for nonpolar solvation analysis. (2012) (48)
On the singular limit in a phase field model of phase transitions (1988) (48)
Spectral analysis and multidimensional stability of traveling waves for nonlocal Allen-Cahn equation (2002) (44)
Asymptotic behavior of stochastic fractional power dissipative equations on Rn (2015) (43)
A numerical scheme for the two phase Mullins-Sekerka problem (1995) (42)
Phase field models for hypercooled solidification (1997) (40)
Spectral analysis of traveling waves for nonlocal evolution equations (2006) (39)
Periodic traveling waves fora nonlocal integro-dierential model (1999) (38)
The existence of travelling wave solutions of a generalized phase-field model (1997) (37)
Dynamics of the 3D fractional Ginzburg–Landau equation with multiplicative noise on an unbounded domain (2016) (36)
Nucleation of Instability of the Meissner State of 3-Dimensional Superconductors (2007) (34)
Heteroclinic solutions of a van der Waals model with indefinite nonlocal interactions (2005) (33)
The minimal molecular surface (2006) (29)
Blow up for a diffusion-advection equation (1989) (29)
On a nonlocal phase-field system (2006) (28)
Solutions to the Nonautonomous Bistable Equation with Specified Morse Index. Part I: Existence (1993) (27)
Tempered random attractors for parabolic equations in weighted spaces (2013) (26)
A Hartman-Grobman theorem for the Cahn-Hilliard and phase-field equations (1994) (26)
Traveling pulses for the Klein-Gordon equation on a lattice or continuum with long-range interaction (2006) (24)
PERIODIC SOLUTIONS OF HIGHER ORDER SYSTEMS (1979) (24)
Heteroclinic orbits for a higher order phase transition problem (1997) (23)
Motion of a Droplet for the Stochastic Mass-Conserving Allen-Cahn Equation (2016) (23)
Solutions of nonlinear elliptic systems with meshed spectra (1980) (19)
Normally hyperbolic invariant manifolds for random dynamical systems: Part I - persistence (2013) (19)
Individual Flux Study via Steady-State Poisson-Nernst-Planck Systems: Effects from Boundary Conditions (2017) (19)
Analysis of a corner layer problem in anisotropic interfaces (2005) (18)
Invariant foliations for random dynamical systems (2014) (17)
Existence and uniqueness for a variational hyperbolic system without resonance (1980) (17)
Global dynamics of boundary droplets (2013) (17)
Mullins-Sekerka motion of small droplets on a fixed boundary (2000) (15)
TRANSITION LAYER SOLUTIONS OF A HIGHER ORDER EQUATION IN AN INFINITE TUBE (1996) (15)
Ion size and valence effects on ionic flows via Poisson-Nernst-Planck models (2017) (14)
Bifurcation and stability of periodic traveling waves for a reaction-diffusion system (1983) (13)
Stabilization of solutions for a class of degenerate equations in divergence form in one space dimension (1988) (13)
Multiphase Solutions to the Vector Allen–Cahn Equation: Crystalline and Other Complex Symmetric Structures (2014) (13)
Geometric singular perturbation theory with real noise (2015) (12)
Mathematical studies of Poisson-Nernst-Planck model for membrane channels: Finite ion size effects without electroneutrality boundary conditions (2019) (12)
Dynamics of ionic flows via Poisson-Nernst-Planck systems with local hard-sphere potentials: Competition between cations. (2020) (12)
Small Permanent Charge Effects on Individual Fluxes via Poisson–Nernst–Planck Models with Multiple Cations (2021) (11)
Entire Solutions with Six-fold Junctions to Elliptic Gradient Systems with Triangle Symmetry (2013) (11)
A SADDLE-POINT THEOREM (1980) (10)
Green's function inequalities for two-point boundary value problems. (1975) (10)
Simulation studies of self-organization of microtubules and molecular motors. (2008) (9)
Nucleation of Instability of the Meissner State of 3-Dimensional Superconductors (2008) (8)
Hilbert space methods for nonlinear elliptic equations (1979) (8)
Maximization of Green’s Function over Classes of Multipoint Boundary Value Problems (1976) (7)
Reduction theorems for a class of semilinear equations at resonance (1982) (7)
Differential Equations and Computational Simulations (1999) (7)
Traveling wave solutions for a nonlocal phase-field system (2002) (7)
Effects on I–V relations from small permanent charge and channel geometry via classical Poisson–Nernst–Planck equations with multiple cations (2021) (7)
Estimates for the eigenvalues of the Jordan product of Hermitian matrices (1984) (7)
Motion of a droplet for the mass-conserving stochastic Allen-Cahn equation (2015) (6)
Growth regulation and the insulin signaling pathway (2013) (6)
Slow Motion Manifolds For A Class of Singular Perturbation Problems: The Linearized Equations (1992) (5)
The spectral collocation method for efficiently solving PDEs with fractional Laplacian (2018) (5)
Bifurcation of periodic travelling waves for a reaction-diffusion system (1982) (5)
Convergence to equilibrium in a reaction-diffusion system (1984) (4)
Gradient Dynamics: Motion Near a Manifold of Quasi-Equilibria (2018) (4)
EQUILIBRIA AND TRAVELING WAVES FOR BISTABLE EQUATIONS WITH NON-LOCAL AND DISCRETE DISSIPATION (Nonlinear Diffusive Systems : Dynamics and Asymptotics) (2000) (4)
Necessary and sufficient conditions for existence.of solutions to equations with noninvertible linear part (1981) (4)
Invariant manifolds of interior multi-spike states for the Cahn-Hilliard equation in higher space dimensions (2016) (4)
Singular fold with real noise (2016) (3)
Travelling waves in radially symmetric parabolic systems (1985) (2)
A VARIATIONAL APPROACH TO SOLVING SEMILINEAR EQUATIONS AT RESONANCE (1982) (2)
Invariant Manifold Theorems with Applications (1986) (1)
Structure of principal eigenvectors and genetic diversity (2011) (1)
Projection methods for nonlinear nodal problems (1977) (1)
Proceedings of the International Conference on Differential Equations and Computational Simulations, Chengdu, China, 13-18 June 1999 (2000) (0)
Lung Cancer, 3rd edition. (2009) (0)
Multiscale Analysis of Self-Organization in Biology (2009) (0)
An invariance principle for a class of monotone systems and application to degenerate parabolic equations (1988) (0)
INVARIANT MANIFOID 'l'HEOREN) WITH APPLICATIONS (1986) (0)
Giant vortex and the breakdown of pinning in a rotating Bose–Einstein condensate (2004) (0)
First International Conference on Recent Advances in Bifurcation Theory and Applications of Dynamical Systems June (2005) (0)
Lung Cancer, 3rd edition (Roth JA, Cox JD, and Hong WK) (2009) (0)
Containment of Solutions to Strongly Coupled Parabolic Systems (1985) (0)
Global Dynamics of Particles Driven by a Nonlinear Reaction-Diffusion Equation (Far-From-Equilibrium Dynamics) (2012) (0)
Existence of global solution for a differential system with initial data in Lp (1999) (0)
The Sixth International Conference on Recent Advances in Applied Dynamical Systems (2012) (0)
Differential equations and applications : proceedings of the US-Chinese Conference : held in Hangzhou, June 24-29, 1996 (1996) (0)
A N INVARIANCE PRINCIPLE FOR A CLASS OF MONOTONE SYSTEMS A N D APPLICATION TO DEGENERATE PARABOLIC EQUATIONS (2008) (0)
Differential Equations and Computational Simulations: Proceedings of the International Conference (2000) (0)

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