Velocity averaging for diffusive transport equations with discontinuous flux
Analysis of PDEs
2022-10-10 v2
Abstract
We consider a diffusive transport equation with discontinuous flux and prove the velocity averaging result under non-degeneracy conditions. In order to achieve the result, we introduce a new variant of micro-local defect functionals which are able to ``recognise'' changes of the type of the equation. As a corollary, we show the existence of a weak solution for the Cauchy problem for nonlinear degenerate parabolic equation with discontinuous flux. We also show existence of strong traces at for so-called quasi-solutions to degenerate parabolic equations under non-degeneracy conditions on the diffusion term.
Cite
@article{arxiv.2008.08310,
title = {Velocity averaging for diffusive transport equations with discontinuous flux},
author = {Marko Erceg and Marin Mišur and Darko Mitrović},
journal= {arXiv preprint arXiv:2008.08310},
year = {2022}
}