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Short Time Uniqueness Results for Solutions of Nonlocal and Non-monotone Geometric Equations

Abstract : We describe a method to show short time uniqueness results for viscosity solutions of general nonlocal and non-monotone second-order geometric equations arising in front propagation problems. Our method is based on some lower gradient bounds for the solution. These estimates are crucial to obtain regularity properties of the front, which allow to deal with nonlocal terms in the equations. Applications to short time uniqueness results for the initial value problems for dislocation type equations, asymptotic equations of a FitzHugh-Nagumo type system and equations depending on the Lebesgue measure of the fronts are presented.
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Submitted on : Wednesday, May 26, 2010 - 5:28:45 PM
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Guy Barles, Olivier Ley, Hiroyoshi Mitake. Short Time Uniqueness Results for Solutions of Nonlocal and Non-monotone Geometric Equations. Mathematische Annalen, Springer Verlag, 2012, 352 (2), pp.409-451. ⟨10.1007/s00208-011-0648-1⟩. ⟨hal-00486802⟩

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