Probabilistic methods for a linear reaction-hyperbolic system with constant coefficients

Abstract

Linear reaction-hyperbolic systems of partial differential equations in one space dimension arise in the study of the physiological process by which materials are transported in nerve cell axons. Probabilistic methods are developed to derive a closed form approximate solution for an initial-boundary value problem of such a system. The approximate solution obtained is a translating solution of a heat equation. An estimate is proved giving the deviation of this approximate traveling wave solution from the exact solution.