Uniqueness results for nonlocal Hamilton-Jacobi equations

被引：15

作者：

Barles, Guy ^{[2
]}

Cardaliaguet, Pierre ^{[1
]}

Ley, Olivier ^{[2
]}

Monteillet, Aurelien ^{[1
]}

机构：

[1] Univ Brest, Math Lab, CNRS, UMR 6205, F-29285 Brest, France

[2] Univ Tours, Lab Math & Phys Theor, F-37200 Tours, France

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2009年 / 257卷 / 05期

关键词：

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; L-1-dependence in time; 2ND-ORDER PARABOLIC EQUATIONS; NEUMANN BOUNDARY-CONDITIONS; PHASE-FIELD-THEORY; VISCOSITY SOLUTIONS; DISLOCATION DYNAMICS; GLOBAL EXISTENCE; L-1; DEPENDENCE; TIME;

D O I：

10.1016/j.jfa.2009.04.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：1261 / 1287

页数：27

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