<b>Long time existence of a class of contact discontinuities for second</b> - doi: 10.5269/bspm.v20i1-2.7522

Abstract

The study of long time existence of classical smooth solutions for second order quasilinear wave equations has received much attention (see e.g. [1] and the references given there). Results were also obtained for continuous semilinear waves with gradient jumps on a characteristic hypersurface in [2] and for C1 quasilinear waves with second order derivatives jumps on a characteristic hypersurface in [3], [4]. In this paper we show how the methods and results of [2] can be extended to a class of continuous weak solutions, with gradient jumps on a characteristic hypersurface, for some second order quasilinear balance laws.