Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations

Details Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations

2008-06-11

arxiv.org/abs/0806.1890v1

Nonlinear Analysis. Theory, Methods and Applications. 71, 7-8 (2009) 2801-2810

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.na.2009.01.156

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.

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