EXISTENCE OF SHOCK WAVE SOLUTIONS TO MULTIDIMENSIONAL HYPERBOLIC SYSTEMS OF CONSERVATION LAWS IN CONTINUUM MECHANICS
Yu.L. Trakhinin
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Keywords: hyperbolic system, conservation laws, shock wave, local existence and uniqueness theorem, gas dynamics, elastodynamics
Abstract
The problem of proving the local-in-time existence and uniqueness of shock wave solutions to hyperbolic systems of conservation laws with many spatial variables is examined. This problem specifically pertains to the task of finding conditions on the initial data, such that, at each point on the surface of the initial shock wave, a smooth solution to the corresponding free boundary problem exists for small time. Examples of systems of conservation laws in continuum mechanics include the equations of gas dynamics and the equations of elastodynamics for compressible neo-Hookean materials.
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