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arXiv · 1709.01410

Relative entropy method for measure-valued solutions in natural sciences

Tomasz Dębiec·Piotr Gwiazda·Kamila Łyczek·Agnieszka Świerczewska-Gwiazda
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Abstract

In this article we describe the applications of the relative entropy framework. In particular uniqueness of an entropy solution is proven for a scalar conservation law, using the notion of measure-valued entropy solutions. Further we survey recent results concerning measure-valued-strong uniqueness for a number of physical systems - incompressible and compressible Euler equations, compressible Navier-Stokes, polyconvex elastodynamics and general hyperbolic conservation laws, as well as long-time asymptotics of the McKendrick-Von Foerster equation.

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Tomasz Dębiec, Piotr Gwiazda, Kamila Łyczek, Agnieszka Świerczewska-Gwiazda. 2017-09-04. Relative entropy method for measure-valued solutions in natural sciences. https://arxiv.org/abs/1709.01410

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