On the existence of solutions to a one-dimensional degenerate nonlinear wave equation

Abstract

This paper is concerned with the degenerate initial–boundary value problem to the one-dimensional nonlinear wave equation utt=((1+u)aux)x which arises in a number of various physical contexts. The global existence of smooth solutions to the degenerate problem was established under relaxed conditions on the initial–boundary data by the characteristic decomposition method. Moreover, we show that the solution is uniformly C1,α continuous up to the degenerate boundary and the degenerate curve is C1,α continuous for α∈(0,min⁡{a1+a,11+a}).