Traveling waves of bistable dynamics in discrete periodic media.
吳菁菁博士國立台灣師範大學數學系 下午 3:00–4:00 鴻經館 107 室Abstract
We study the existence, uniqueness, and stability of traveling waves for a system of ordinary differential equations with bistable nonlinearity in discrete periodic media.
This system arises from a spatial discrete version of some semilinear parabolic equations with periodic nonlinearity. The main tools to derive the uniqueness and asymptotic stability are comparison principle, spectrum analysis of the linearized operator around a steady state, and the construction of suitable super/subsolutions. To derive the existence of traveling wave, we first convert the system to an integral equation. Then we establish the existence of traveling wave for this system of ordinary differential equations.