Kinetic solutions for nonlocal scalar conservation laws
Analysis of PDEs
2017-05-01 v1
Abstract
This work is devoted to examine the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal super-critical diffusion operator. Our proof for uniqueness is based upon the analysis on a microscopic contraction functional and the existence is enabled by a parabolic approximation. As an illustration, we obtain the existence and uniqueness of kinetic solutions for the generalized fractional Burgers-Fisher type equations. Moreover, we demonstrate the kinetic solutions' Lipschitz continuity in time, and continuous dependence on nonlinearities and L\'{e}vy measures.
Cite
@article{arxiv.1704.08784,
title = {Kinetic solutions for nonlocal scalar conservation laws},
author = {Jinlong Wei and Jinqiao Duan and Guangying Lv},
journal= {arXiv preprint arXiv:1704.08784},
year = {2017}
}
Comments
22 pages