Abstract: We considered the third boundary value problem of nonlinear singularly perturbed wave equation. Firstly, the outer solution was constructed by using singular perturbation method. Secondly,  correction terms of the shock layer, initial layer and boundary layer were obtained by using the stretched variables. Finally,  the asymptotic expansion of solution to problem was given, and the uniform validity of its asymptotic solution was proved.

Key words: nonlinear wave, third boundary value problem, outer solution, correction term, singular perturbation, asymptotic, shock wave