English

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}
}