Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations
Analysis of PDEs
2010-02-10 v1
Abstract
In this article, we provide existence results for a general class of nonlocal and nonlinear second-order parabolic equations. The main motivation comes from front propagation theory in the cases when the normal velocity depends on the moving front in a nonlocal way. Among applications, we present level-set equations appearing in dislocations' theory and in the study of Fitzhugh-Nagumo systems.
Keywords
Cite
@article{arxiv.0806.1890,
title = {Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations},
author = {Guy Barles and Pierre Cardaliaguet and Olivier Ley and Aurélien Monteillet},
journal= {arXiv preprint arXiv:0806.1890},
year = {2010}
}