Brian Moore, University of Central Florida


Solutions and Behavior of Lattice Differential Equations

Abstract: Lattice differential equations are often viewed as spatial discretizations of time dependent partial differential equations, where the solution behavior of one converges to that of the other by variation of a small parameter. Yet, many physical systems are more appropriately modeled with lattice differential equations in which the parameter is not small and is also not related to the lattice spacing. Both points of view will be presented in this talk by way of some important examples. Specifically, phase separation in spatially discrete Cahn-Hilliard equations is largely dependent upon a small parameter, while conservation laws in spatially discrete Hamiltonian equations demonstrate occasional dependence on this parameter. Finally, wave front solutions of a spatially discrete Nagumo equation exhibit speed-up and slow-down, or even propagation failure, when the parameter is allowed to depend on the lattice position but not lattice spacing.


Address: Department of Mathematics, University of Central Florida, 4000 Central Florida Blvd, Orlando, FL 32816-1364. Go to Professor Moore's website.