Convergence of approximation schemes for nonlocal front propagation equations

Author:
Aurélien Monteillet

Journal:
Math. Comp. **79** (2010), 125-146

MSC (2000):
Primary 65M12, 53C44, 35K65, 70H20, 49L25

DOI:
https://doi.org/10.1090/S0025-5718-09-02270-4

Published electronically:
June 8, 2009

MathSciNet review:
2552220

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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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Additional Information

**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:
https://doi.org/10.1090/S0025-5718-09-02270-4

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

Published electronically:
June 8, 2009

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.