位错型方程的弱解
Weak Solutions for Dislocation Type Equations
摘要：
我们描述了G. Barles，P. Cardaliaguet，R.作者和作者最近。他们关心的是在晶体中位错线动力学研究中产生的非局部程函方程。这些方程是非局部的，但也是非单调的。我们使用弱解的概念来提供所有时间的解。然后，我们讨论了这些弱解与经典黏性解之间的联系，并给出了一些特殊情况下的唯一性结果。给出了唯一性的一个反例。
英文摘要：
We describe recent results obtained by G. Barles, P. Cardaliaguet, R. Monneau and the author recently. They are concerned with nonlocal Eikonal equations arising in the study of the dynamics of dislocation lines in crystals. These equations are nonlocal but also non monotone. We use a notion of weak solution to provide solutions for all time. Then, we discuss the link between these weak solutions and the classical viscosity solutions, and state some uniqueness results in particular cases. A counter-example to uniqueness is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
