Global Existence for a System of Non-Linear and Non-Local Transport Equations Describing the Dynamics of Dislocation Densities
Global Existence for a System of Non-Linear and Non-Local Transport Equations Describing the Dynamics of Dislocation Densities
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DOI：
10.1007/s00205-009-0235-8
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发表时间：
2009-01
影响因子：
2.5
通讯作者：
M. Cannone;A. Hajj;R. Monneau;Francis Ribaud
中科院分区：
文献类型：
--
作者：
M. Cannone;A. Hajj;R. Monneau;Francis Ribaud
在本文中，我们研究了描述位错密度动态的 Groma-Balogh 模型的全局时间存在问题。该模型是一个二维模型，其中位错密度满足输运方程组，使得速度矢量场是材料中的剪切应力，求解弹性方程。该剪切应力可以表示为位错密度的某种 Riesz 变换。证明该结果的主要工具是该系统的熵的存在。
In this paper, we study the global in time existence problem for the Groma-Baloghmodel describing the dynamics of dislocation densities. This model is a two-dimensional model where the dislocation densities satisfy a system of transport equations such that the velocity vector field is the shear stress in the material, solving the equations of elasticity. This shear stress can be expressed as some Riesz transform of the dislocation densities. The main tool in the proof of this result is the existence of an entropy for this system.