晶体位错动力学的长时间行为
Long-time behavior for crystal dislocation dynamics
摘要：
本文描述了一个演化型非局部方程解的渐近态，它具有周期晶体中原子位错函数的物理意义。更精确地说，我们可以精确地描述在“粒子碰撞”之后出现的对位错函数的“平滑效应”（粗略地说，两个相反的过渡层达到平均值），并且，以这种方式，我们可以将原子位错函数捕获在过渡层的叠加之间，随着时间的推移，接近常数函数或单个异宿（取决于初始过渡层的取向的代数性质）。结果被赋予了明确的和定量的估计，作为副产品，我们表明，控制过渡层演化的粒子的ODE系统不允许固定的解决方案（即，粗略地说，过渡层总是移动）。
英文摘要：
We describe the asymptotic states for the solutions of a nonlocal equation of evolutionary type, which have the physical meaning of the atom dislocation function in a periodic crystal. More precisely, we can describe accurately the "smoothing effect" on the dislocation function occurring slightly after a "particle collision" (roughly speaking, two opposite transitions layers average out) and, in this way, we can trap the atom dislocation function between a superposition of transition layers which, as time flows, approaches either a constant function or a single heteroclinic (depending on the algebraic properties of the orientations of the initial transition layers). The results are endowed of explicit and quantitative estimates and, as a byproduct, we show that the ODE systems of particles that governs the evolution of the transition layers does not admit stationary solutions (i.e., roughly speaking, transition layers always move).
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