Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations
arXiv:0806.1890 · doi:10.1016/j.na.2009.01.156
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.