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arXiv · 0806.1890

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

Guy Barles·Pierre Cardaliaguet·Olivier Ley·Aurélien Monteillet
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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.

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Guy Barles, Pierre Cardaliaguet, Olivier Ley, Aurélien Monteillet. 2008-06-11. Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations. https://doi.org/10.1016/j.na.2009.01.156

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