Monday, May 24

Analysis and Computation of Bistable Differential-Difference Equations

10:00 AM-12:00 PM
Room: Maybird

We focus on recent developments in the analysis and computation of bistable differential-difference equations, including reaction-diffusion and Cahn-Hilliard like equations. The problem areas include integrodifferential models for both spatially discrete and spatially continuous systems, a Fredholm theory for equations with backward and forward delays to analyze the structure of traveling wave solutions and that forms the basis for a numerical technique for the computation of traveling waves, and analysis and computational techniques for equilibrium solutions of spatially discrete Cahn-Hilliard equations. An important issue to be addressed is the relative impact of both spatially discrete and continuous terms on the dynamics.

Erik S. Van Vleck
Colorado School of Mines

10:00-10:25 A Discrete Convolution Model for Phase Transitions
Peter Bates, Brigham Young University; and Adam Chmaj, Utah State University
10:30-10:55 A Variant of Newton's Method for the Computation of Traveling Wave Solutions of Differential-Difference Equations
Christopher Elmer, National Institute of Standards and Technology, Gaithersburg; and Erik S. Van Vleck, Organizer
11:00-11:25 Mosaic Solutions and Entropy for Spatially Discrete Cahn- Hilliard Equations
K. A. Abell and Anthony R. Humphries, University of Sussex, Brighton, United Kingdom; and Erik S. Van Vleck, Organizer
11:30-11:55 Crystallographic Pinning: Direction Dependent Traveling Waves in Higher Dimensional Lattices
John Mallet-Paret, Brown University

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MMD, 2/9/99
LMH, 1/8/99; tjf, 2/2/99