Gibb's minimization principle for approximate solutions of scalar conservation laws
Analysis of PDEs
2016-08-01 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1607.08852,
title = {Gibb's minimization principle for approximate solutions of scalar conservation laws},
author = {Misha Perepelitsa},
journal= {arXiv preprint arXiv:1607.08852},
year = {2016}
}