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arXiv · 2006.10699

Existence of solutions for the surface electromigration equation

Felipe Linares·Ademir Pastor·Marcia Scialom
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Abstract

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.

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Felipe Linares, Ademir Pastor, Marcia Scialom. 2020-06-18. Existence of solutions for the surface electromigration equation. https://doi.org/10.1088/1361-6544/abfae6

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