Global B V solution for a non-local coupled system modeling the dynamics of dislocation densities

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

El Hajj, Ahmad¹  Ibrahim, Hassan²  Rizik, Vivian^1,2 

[1] Univ Technol Compiegne, LMAC, F-60205 Compiegne, France

[2] Lebanese Univ, Math Dept, Fac Sci 1, Hadath, Lebanon

关键词: Hamilton-Jacobi system;    Non-local eikonal system;    Non-local transport system;    BV estimate;    Discontinuous viscosity solution;    Dislocation dynamics;   

DOI  :  10.1016/j.jde.2017.10.004

来源: Elsevier

【 摘 要 】

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. (c) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free