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Short time uniqueness results for solutions of nonlocal and non-monotone geometric equations. (English) Zbl 1246.35013
The authors 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. Their methods is based on some lower gradient bounds for the solution. This results are then used to obtain 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.

MSC:
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35K15 Initial value problems for second-order parabolic equations
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
45K05 Integro-partial differential equations
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
35D40 Viscosity solutions to PDEs
35R09 Integral partial differential equations
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