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

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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Submitted on : Wednesday, June 11, 2008 - 4:47:15 PM
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Guy Barles, Pierre Cardaliaguet, Olivier Ley, Aurélien Monteillet. Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2009, 71 (7-8), pp.2801-2810. ⟨10.1016/j.na.2009.01.156⟩. ⟨hal-00287372⟩

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