Peierls-Nabarro模型作为Frenkel-Kontorova模型的极限
The Peierls-Nabarro model as a limit of a Frenkel-Kontorova model
摘要：
研究了全过阻尼Frenkel-Kontorova模型在$n\geq 1.$维上的推广.该模型描述了晶体中每个原子位置的演化，在数学上由一个耦合的一阶常微分方程的无限系统给出.我们证明了，对于一个适当的重新标度的这个模型，该解决方案收敛到Peierls-Nabarro模型，这是一个耦合系统的两个PDE（通常是一个椭圆型PDE在域的边界上的发展PDE的域）。这种从离散模型到连续模型的转变是在黏性解的框架内完成的。
英文摘要：
We study a generalization of the fully overdamped Frenkel-Kontorova model in dimension $n\geq 1.$ This model describes the evolution of the position of each atom in a crystal, and is mathematically given by an infinite system of coupled first order ODEs. We prove that for a suitable rescaling of this model, the solution converges to the solution of a Peierls-Nabarro model, which is a coupled system of two PDEs (typically an elliptic PDE in a domain with an evolution PDE on the boundary of the domain). This passage from the discrete model to a continuous model is done in the framework of viscosity solutions.
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。
