Singular Perturbations for a Semilinear Hyperbolic Equation

Abstract

The Cauchy problem for a semilinear hyperbolic equation with a small parameter is considered. The reduced problem is of parabolic type and, although there is no reduction of order, there is an initial layer. An asymptotic solution with boundary layer corrections is constructed and, for a restricted class of nonlinearities, is shown to be uniformly asymptotically valid for sets bounded in the time direction.