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Stability of multidimensional shocks. (English) Zbl 1017.35075
Freistühler, Heinrich (ed.) et al., Advances in the theory of shock waves. Boston, MA: Birkhäuser. Prog. Nonlinear Differ. Equ. Appl. 47, 25-103 (2001).
This article is devoted to the study of shock waves for systems of multidimensional conservation laws. In contrast to the 1D case, in higher space dimensions there is no general existence theorem for solutions which allows discontinuities. The aim of the author is to study the existence and stability of the simplest pattern of a single wave front \(\Sigma\), separating two states \(u^+\) and \(u^-\), which depend smoothly on the space-time variable \(x\). The analysis of the author is applicable to much more general situations and the author studies curved fronts as well.
For the entire collection see [Zbl 0966.00009].

35L67 Shocks and singularities for hyperbolic equations
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35L65 Hyperbolic conservation laws