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arXiv · 1408.0815

Relative entropy in hyperbolic relaxation for balance laws

Alexey Miroshnikov·Konstantina Trivisa
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Abstract

We present a general framework for the approximation of systems of hyperbolic balance laws. The novelty of the analysis lies in the construction of suitable relaxation systems and the derivation of a delicate estimate on the relative entropy. We provide a direct proof of convergence in the smooth regime for a wide class of physical systems. We present results for systems arising in materials science, where the presence of source terms presents a number of additional challenges and requires delicate treatment. Our analysis is in the spirit of the framework introduced by Tzavaras [A. Tzavaras, Commun. Math. Sci., 3-2, 2005] for systems of hyperbolic conservation laws.

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Alexey Miroshnikov, Konstantina Trivisa. 2014-08-04. Relative entropy in hyperbolic relaxation for balance laws. https://doi.org/10.4310/cms.2014.v12.n6.a2

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