Formation-construction of shock in compressive simple wave \(N\times N\) hyperbolic system (Q2759772)

This paper is the continuation of a series by the author et al. on the formation of shock waves in one space dimension. The previous ones [Advances in nonlinear partial differential equations and related areas, Beijing, 1997, World Scientific Publishing, 45-66 (1998; Zbl 0929.35091); Sci. China, Ser. A 44, 1139-1147 (2001; Zbl 1054.35027); J. Math. Phys. 42, 1154-1172 (2001; Zbl 1053.76035)] were mainly concerned with gas dynamics. Here a general hyperbolic system of conservation laws is considered. The situation under study is starting from a simple wave, when the envelop of the corresponding (straight) characteristic lines has a cusp at some time \(t_0\). Under non-degeneracy assumptions, the Cauchy problem is solved for \(t>t_0\) close to \(t_0\) by means of a weak solution containing a single shock. The method involves an iterative scheme. Part of the technical material is borrowed from the papers quoted above and from the paper by \textit{M.-P. Lebaud} [J. Math. Pures Appl., IV. Sér. 73, 523-565 (1994; Zbl 0832.35092)] .NEWLINENEWLINEFor the entire collection see [Zbl 0969.00056].