Global existence results and uniqueness for dislocation equations

Barles G; Cardaliaguet P; Ley O; Monneau R

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Global existence results and uniqueness for dislocation equations

机译：整体存在结果和位错方程的唯一性

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We are interested in nonlocal eikonal equations arising in the study of the dynamics of dislocation lines in crystals. For these nonlocal but also nonmonotone equations, only the existence and uniqueness of Lipschitz and local-in-time solutions were available in some particular cases. In this paper, we propose a definition of weak solutions for which we are able to prove the existence for all time. Then we discuss the uniqueness of such solutions in several situations, both in the monotone and the nonmonotone case.

机译：我们对晶体中位错线动力学的研究中产生的非局部本征方程感兴趣。对于这些非局部但非单调方程，在某些特定情况下，只有Lipschitz的存在性和唯一性以及局部时间解。在本文中，我们提出了一个弱解的定义，我们可以证明该弱解一直存在。然后，我们讨论在单调和非单调情况下，在几种情况下此类解决方案的唯一性。

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《SIAM Journal on Mathematical Analysis》 |2008年第1期|共26页
作者
Barles G; Cardaliaguet P; Ley O; Monneau R;
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正文语种 eng
中图分类数学分析;
关键词
nonlocal Hamilton-Jacobi equations; dislocation dynamics; nonlocal front propagation; level-set approach; geometrical properties; lower-bound gradient estimate; viscosity solutions; eikonal equation; L-1-dependence in time; HAMILTON-JACOBI EQUATIONS; NEUMANN BOUNDARY-CONDITIONS; VISCOSITY SOLUTIONS; PARABOLIC EQUATIONS; FRONT PROPAGATION; TIME; DYNAMICS; SETS;

机译：非局部Hamilton-Jacobi方程;位错动力学;非局部前沿传播;水平集方法;几何特性;下界梯度估计;粘度解;本征方程;L-1时间依赖性;HAMILTON-JACOBI方程;NEUMANN边界条件;粘度解;抛物方程;前传播;时间;动力学;集合;

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5. Global existence, uniqueness and stability of a quasilinear hyperbolic equation with boundary dissipation. [D] . Ong, John. 1998

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6. Existence and Uniqueness of Solution for a Class of Stochastic Differential Equations [O] . Junfei Cao, Zaitang Huang, Caibin Zeng 2013

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7. Global Existence Results and Uniqueness for Dislocation Equations [O] . Barles, Guy, Cardaliaguet, Pierre, Ley, Olivier, 2009

机译：位错方程的整体存在性和唯一性

Global existence results and uniqueness for dislocation equations

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