Uniqueness results for nonlocal Hamilton–Jacobi equations
Barles, Guy; Cardaliaguet, Pierre; Ley, Olivier; Monteillet, Aurélien (2009), Uniqueness results for nonlocal Hamilton–Jacobi equations, Journal of Functional Analysis, 257, 5, p. 1261-1287. http://dx.doi.org/10.1016/j.jfa.2009.04.014
Type
Article accepté pour publication ou publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00264757/fr/Date
2009Journal name
Journal of Functional AnalysisVolume
257Number
5Publisher
Elsevier
Pages
1261-1287
Publication identifier
Metadata
Show full item recordAbstract (EN)
We are interested in nonlocal eikonal equations describing the evolution of interfaces moving with a nonlocal, non-monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends existing results for dislocation dynamics. It also provides the first uniqueness result for a Fitzhugh–Nagumo system. The key ingredients are some new perimeter estimates for the evolving fronts as well as some uniform interior cone property for these fronts.Subjects / Keywords
Nonlocal Hamilton–Jacobi equations; Dislocation dynamics; Fitzhugh–Nagumo system; Nonlocal front propagation; Level-set approach; Geometrical properties; Lower-bound gradient estimate; Viscosity solutions; Eikonal equation; L1-dependence in timeRelated items
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