Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions

Partial differential equations of parabolic type

John S. Maybee · Journal of the Franklin Institute · 1965 · 3.3K citations

Natural Sciences, Mathematics, Differential Equations +11

Traveling Waves in a Convolution Model for Phase Transitions

Peter W. Bates, Paul C. Fife, Xiaofeng Ren et al. · Archive for Rational Mechanics and Analysis · 1997 · 559 citations

Natural Sciences, Physics, Computational Physics +10

Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations

Xinfu Chen · Advances in Differential Equations · 1997 · 453 citations · Full text

Natural Sciences, Mathematics, Differential Equations +16

A Discrete Convolution Model¶for Phase Transitions

Peter W. Bates, Adam Chmaj · Archive for Rational Mechanics and Analysis · 1999 · 221 citations

Natural Sciences, Materials Science, Mathematics +11

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

Peter W. Bates, Adam Chmaj · Journal of Statistical Physics · 1999 · 210 citations

Natural Sciences, Mathematics, Physics +13