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We prove existence of minimizing movements for the
dislocation dynamics evolution law of a propagating front, in which the normal velocity of the front is the sum of a non-local term and a mean curvature term. We prove that any such minimizing movement is a weak solution of this evolution law, in a sense related to viscosity
solutions of the corresponding level-set equation. We also prove the
consistency of this approach, by showing that any minimizing movement
coincides with the smooth evolution...
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