On a Hyperbolic System of Conservation Laws Which Is Not Strictly Hyperbolic.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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We study a system of quasilinear hyperbolic conservation laws which is hyperbolic but not strictly hyperbolic. Such systems arise naturally in continuum mechanics such as elastic, multiphase flows. We are interested mainly in the large time behavior of the solution. Due to the nonlinearity of the system and the entropy condition, solutions converge to very simple elementary waves. Nonstrict hyperbolicity of the system amy cause a stronger nonlinear interactions between waves pertaining to different families in particular, such interactions may regularize linear waves in the solution. The solutions are constructed using the random choice method. Author
- Theoretical Mathematics
- Fluid Mechanics