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

Monteillet, Aurélien; Ley, Olivier; Cardaliaguet, Pierre; Barles, Guy (2009), Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations, Nonlinear Analysis: Theory, Methods & Applications, 71, 7-8, p. 2801-2810. http://dx.doi.org/10.1016/j.na.2009.01.156

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00287372/fr/
Date
2009
Journal name
Nonlinear Analysis: Theory, Methods & Applications
Volume
71
Number
7-8
Publisher
Elsevier
Pages
2801-2810
Publication identifier
Metadata
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Author(s)
Monteillet, Aurélien
Ley, Olivier
Cardaliaguet, Pierre
Barles, Guy
Abstract (EN)
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 dislocation theory and in the study of Fitzhugh–Nagumo systems.
Subjects / Keywords
L1-dependence in time; Viscosity solutions; Nonlocal front propagation; Fitzhugh–Nagumo system; Dislocation dynamics; Existence results; Nonlocal Hamilton–Jacobi Equations