Abstract
This series of lectures is devoted to the study of shock waves for systems of multidimensional conservation laws. In sharp contrast with one-dimensional problems, in higher space dimensions there is no general existence theorem for solutions which allow discontinuities. Our goal is to study the existence and the stability of the simplest pattern of a single wave front ∑, separating two states u + and u -, which depend smoothly on the space-time variables x. For example, our analysis applies to perturbations of planar shocks. They are special solutions given by constant states separated by a planar front. Given a multidimensional perturbation of the initial data or a small wave im**ing on the front, we study the following stability problem. Is there a local solution with the same wave pattern? Similarly, a natural problem is to investigate the multidimensional stability of one-dimensional shock fronts. However, the analysis applies to much more general situations and the main subject is the study of curved fronts.
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Métivier, G. (2001). Stability of Multidimensional Shocks. In: Freistühler, H., Szepessy, A. (eds) Advances in the Theory of Shock Waves. Progress in Nonlinear Differential Equations and Their Applications, vol 47. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0193-9_2
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DOI: https://doi.org/10.1007/978-1-4612-0193-9_2
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