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

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}).