English

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}
}