A semilinear wave equation with space–time dependent coefficients and a memory boundarylike antiperiodic condition: A low-frequency asymptotic expansion

Abstract

This paper studies a low-frequency asymptotic expansion for a unique strong solution to an initial-boundary value problem of a semilinear wave equation. This equation admits space–time dependent coefficients and a memory boundarylike antiperiodic condition. For some small parameters from coefficients of this semilinear wave equation and of boundary conditions, we approximate a unique strong solution to this problem by a polynomial of these parameters, and coefficients of this polynomial are strong solutions of a sequence of well-defined linear initial-boundary value problems.