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Long time existence of a class of contact discontinuities for second order hyperbolic balance laws

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Author(s): Paul Godin

Journal: Boletim da Sociedade Paranaense de Matemática
ISSN 0037-8712

Volume: 20;
Issue: 1-2;
Start page: 51;
Date: 2002;
Original page

Keywords: second order quasilinear wave equations | semilinear waves with gradient jumps on a characteristic hypersurface.

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 waveswith 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.
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