Topological Methods in Nonlinear Analysis

Relative entropy method for measure-valued solutions in natural sciences

Tomasz Dębiec, Piotr Gwiazda, Kamila Łyczek, and Agnieszka Świerczewska-Gwiazda

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Abstract

We describe the applications of the relative entropy framework introduced in [10]. In particular the 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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 52, Number 1 (2018), 311-335.

Dates
First available in Project Euclid: 18 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1534557632

Digital Object Identifier
doi:10.12775/TMNA.2018.027

Mathematical Reviews number (MathSciNet)
MR3867990

Zentralblatt MATH identifier
07029872

Citation

Dębiec, Tomasz; Gwiazda, Piotr; Łyczek, Kamila; Świerczewska-Gwiazda, Agnieszka. Relative entropy method for measure-valued solutions in natural sciences. Topol. Methods Nonlinear Anal. 52 (2018), no. 1, 311--335. doi:10.12775/TMNA.2018.027. https://projecteuclid.org/euclid.tmna/1534557632


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