描述位错密度动力学的非线性非局部输运方程组的整体存在性
Global existence for a system of non-linear and non-local transport equations describing the dynamics of dislocation densities
摘要：
本文研究了描述位错密度动力学的Groma-Balogh模型在时间上的整体存在性问题。该模型是二维模型，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，从而求解弹性方程。这种剪应力可以表示为位错密度的某种Riesz变换。证明这个结果的主要工具是这个系统熵的存在性
英文摘要：
In this paper, we study the global in time existence problem for the Groma-Balogh model 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
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