论文标题
存在表面电气移动方程的解决方案
Existence of solutions for the surface electromigration equation
论文作者
论文摘要
我们考虑了一种描述纳米导体中电迁移的模型，称为表面电气移动（SEM）方程。我们的目的是从两个不同的角度从Sobolev空间中为相关的初始价值问题建立本地适合性。在第一个中，我们研究了纯库奇问题，并在$ h^s（\ mathbb {r}^2）$，$ s> 1/2 $中建立本地供应良好。在第二个问题中，我们研究了在较少规则的空间中的Korteweg-de Vries孤立波动的背景下的Cauchy问题。为了获得我们的结果，我们利用解决方案的解决方案的平滑属性，与Zakharov-Kuznetsov方程相对应。对于前一种问题，我们在Molinet和Pilod建立的傅立叶限制空间中使用双线性估计值。
We consider a model that describes electromigration in nanoconductors known as surface electromigration (SEM) equation. Our purpose here is to establish local well-posedness for the associated initial value problem in Sobolev spaces from two different points of view. In the first one, we study the pure Cauchy problem and establish local well-posedness in $H^s(\mathbb{R}^2)$, $s>1/2$. In the second one, we study the Cauchy problem on the background of a Korteweg-de Vries solitary traveling wave in a less regular space. To obtain our results we make use of the smoothing properties of solutions for the linear problem corresponding to the Zakharov-Kuznetsov equation for the latter problem. For the former problem we use bilinear estimates in Fourier restriction spaces established by Molinet and Pilod.
