arXiv:1607.08852 Abstract | arXiv Analytics

arXiv:1607.08852 [math.AP]Abstract References Reviews Resources

Gibb's minimization principle for approximate solutions of scalar conservation laws

Published 2016-07-29Version 1

In this work we study variational properties of approximate solutions of scalar conservation laws. Solutions of this type are described by a kinetic equation which is similar to the kinetic representation of admissible weak solutions due to Lions-Perthame-Tadmor, but also retain small scale non-equilibrium behavior. We show that approximate solutions can be obtained from a BGK-type equation with equilibrium densities satisfying Gibb's entropy minimization principle.

Categories: math.AP

Keywords: scalar conservation laws, approximate solutions, gibbs minimization principle, gibbs entropy minimization principle, small scale non-equilibrium behavior

Related articles: Most relevant | Search more

arXiv:1002.1979 [math.AP] (Published 2010-02-09)

Scalar conservation laws with nonconstant coefficients with application to particle size segregation in granular flow

Lindsay B. H. May, Michael Shearer, Karen E. Daniels

arXiv:1309.1931 [math.AP] (Published 2013-09-08)

Scalar conservation laws with rough (stochastic) fluxes

Pierre-Louis Lions, Benoit Perthame, Panagiotis E. Souganidis

arXiv:2306.13341 [math.AP] (Published 2023-06-23)

Viscous shocks and long-time behavior of scalar conservation laws

Thierry Gallay, Arnd Scheel