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Nonlocal front propagation problems and Hamilton-Jacobi equations
This talk is concerned with existence and uniqueness results
for some nonlocal Hamilton-Jacobi equations. These equations
arise when using the level-set approach to describe front
propagation problems. Two model problems are considered,
the dynamics of dislocations and the asymptotics of a
FitzHugh-Nagumo system. In both cases, the velocity is
nonlocal since it depends on the whole set enclosed by
the front. Moreover, the motion is nonmonotone and
we cannot use maximum principle type arguments.
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