Existence of strong travelling wave profiles to 2×2 systems of viscous conservation laws

Yang, Tong; Zhang, Mei; Zhu, Changjiang

doi:10.1090/S0002-9939-07-08747-3

Existence of strong travelling wave profiles to $2\times 2$ systems of viscous conservation laws
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by Tong Yang, Mei Zhang and Changjiang Zhu PDF

Proc. Amer. Math. Soc. 135 (2007), 1843-1849 Request permission

Abstract:

In this paper, we prove the existence of strong travelling wave profiles for a class of $2\times 2$ viscous conservation laws when the corresponding invisid systems are hyperbolic. Besides some technical assumptions, the only main assumption is the hyperbolicity. Therefore, the existence theory can be applied to systems which are not strictly hyperbolic. Moreover, the characteristic fields can be neither genuinely nonlinear nor linearly degenerate.

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