The Asymptotic Behavior of a Free Boundary Arising from a Bistable Reaction-Diffusion Equation

摘要

The mathematical equation studied here has been considered as a model for a variety of physical phenomena including population genetics and nerve conduction. Of primary interest is the eventual behavior of solutions of this equation. One expects that for sufficiently large initial datum the solutions should eventually look like some type of wave traveling with constant shape and velocity. In the case of nerve conduction, for example, the initial datum may correspond to a stimulus applied to the nerve axon. Physiologically, it has been demonstrated that if this stimulus is greater than some threshold amount, then a signal will propagate down the axon with a speed independent of the initial stimulus. In this paper we demonstrate that the equation under study supports solutions exhibiting similar behaviors. (Author)