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arxiv: 1210.4072 · v1 · pith:YMICR2XF · submitted 2012-10-15 · math.AP · math-ph· math.MP

On the well-posedness of a 2D nonlinear and nonlocal system arising from the dislocation dynamics

Dong Li , Changxing Miao , Liutang Xue This is my paper

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classification math.AP math-phmath.MP
keywords nonlocalwell-posednessdislocationdynamicsnonlinearsystemarisingcases
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In this paper we consider a 2D nonlinear and nonlocal model describing the dynamics of the dislocation densities. We prove the local well-posedness of strong solution to this system in the suitable functional framework, and we show the global well-posedness for some dissipative cases by the method of nonlocal maximum principle.

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