Asymptotic theory for weakly non-linear wave equations in semi-infinite domains

Abstract

We prove the existence and uniqueness of solutions of a class of weakly non-linear wave equations in a semi-infinite region $0le x$, $t< L/sqrt{|epsilon|}$ under arbitrary initial and boundary conditions. We also establish the asymptotic validity of formal perturbation approximations of the solutions in this region.

Keywords

• Multiple scale
• perturbation
• non-linear
• waves
• asymptotic.