Existence of solutions for the surface electromigration equation
| Autor: | Felipe Linares, Marcia Scialom, Ademir Pastor |
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| Rok vydání: | 2021 |
| Předmět: |
Cauchy problem
Surface (mathematics) Applied Mathematics 010102 general mathematics Mathematical analysis Mathematics::Analysis of PDEs General Physics and Astronomy Bilinear interpolation Statistical and Nonlinear Physics 01 natural sciences 010101 applied mathematics Sobolev space symbols.namesake Mathematics - Analysis of PDEs Nonlinear Sciences::Exactly Solvable and Integrable Systems Fourier transform FOS: Mathematics symbols Initial value problem Regular space 0101 mathematics Mathematical Physics Smoothing Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Nonlinearity. 34:5213-5233 |
| ISSN: | 1361-6544 0951-7715 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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