Well-posedness for conservation laws with spatial heterogeneities and a study of BV regularity
Analysis of PDEs
2020-10-27 v1
Abstract
In this article, we consider scalar conservation laws with fluxes having spatial discontinuities and possible flat regions and study the following three aspects: (i) existence, (ii) uniqueness and (iii) BV regularity of solutions. We propose a uniqueness condition and prove existence of a weak solution via the method of wave front tracking. In the later part of the article, a BV bound of the solution is achieved under a suitable condition on the initial data and flux. We construct two counterexamples showing BV blow-up of the solution which proves the optimality on the assumptions
Keywords
Cite
@article{arxiv.2010.13695,
title = {Well-posedness for conservation laws with spatial heterogeneities and a study of BV regularity},
author = {Shyam Sundar Ghoshal and John D. Towers and Ganesh Vaidya},
journal= {arXiv preprint arXiv:2010.13695},
year = {2020}
}