Global BV solution for a non-local coupled system modeling the dynamics of dislocation densities |
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Affiliation: | 1. Université de Technologie de Compiègne, LMAC, 60205 Compiègne Cedex, France;2. Faculty of Sciences (I), Mathematics Department, Lebanese University, Hadath, Lebanon |
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Abstract: | In this paper, we study a non-local coupled system arising in the modeling of the dynamics of dislocation densities in crystals. For this system, the global existence and uniqueness are available only for continuous viscosity solutions. In the present paper, we investigate the global time existence of this system by considering BV initial data. Based on a fundamental uniform BV estimate and the finite speed of propagation property of this system, we show, in a particular setting, the global existence of discontinuous viscosity solutions of this problem. |
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Keywords: | Hamilton–Jacobi system Non-local eikonal system Non-local transport system Discontinuous viscosity solution Dislocation dynamics |
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