Mathematics of Computation

Author(s): Aurélien Monteillet.
Journal: Math. Comp. 79 (2010), 125-146.
MSC (2000): Primary 65M12, 53C44, 35K65, 70H20, 49L25
Posted: June 8, 2009
Retrieve article in: PDF

Abstract: We provide a convergence result for numerical schemes approximating nonlocal front propagation equations. Our schemes are based on a recently investigated notion of a weak solution for these equations. We also give examples of such schemes, for a dislocation dynamics equation, and for a FitzHugh-Nagumo type system.

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Aurélien Monteillet
Affiliation: Université de Bretagne Occidentale, UFR Sciences et Techniques, 6 av. Le Gorgeu, BP 809, 29285 Brest, France
Email: aurelien.monteillet@univ-brest.fr

DOI: 10.1090/S0025-5718-09-02270-4
PII: S 0025-5718(09)02270-4
Keywords: Approximation schemes, front propagations, level-set approach, nonlocal Hamilton-Jacobi equations, second-order equations, viscosity solutions, $L^1$ dependence in time, dislocation dynamics, FitzHugh-Nagumo system.
Received by editor(s): September 22, 2008
Received by editor(s) in revised form: February 13, 2009
Posted: June 8, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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