Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/16905
Título: | On the critical KdV equation with time-oscillating nonlinearity |
Autor(es): | Carvajal, Xavier Panthee, Mahendra Prasad Scialom, Marcia |
Palavras-chave: | Korteweg-de vries equation Cauchy problem Local & global well-posedness |
Data: | 2011 |
Editora: | Khayyam Publishing |
Revista: | Differential and Integral Equations |
Resumo(s): | We investigate the initial value problem (IVP) associated to the equation \begin{equation*} u_{t}+\partial_x^3u+g(\omega t)\partial_x(u^5) =0, \end{equation*} where $g$ is a periodic function. We prove that, for given initial data $\phi \in H^1(\mathbb{R})$, as $|\omega|\to \infty$, the solution $u_{\omega}$ converges to the solution $U$ of the initial value problem associated to \begin{equation*} U_{t}+\partial_x^3U+m(g)\partial_x(U^5) =0, \end{equation*} with the same initial data, where $m(g)$ is the average of the periodic function $g$. Moreover, if the solution $U$ is global and satisfies $\|U\|_{L_x^5L_t^{10}}<\infty$, then we prove that the solution $u_{\omega}$ is also global provided $|\omega|$ is sufficiently large. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/16905 |
ISSN: | 0893-4983 |
Versão da editora: | http://www.aftabi.com/die-24a.html |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
Aparece nas coleções: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
---|---|---|---|---|
CPS-final3.pdf | Documento principal | 281,59 kB | Adobe PDF | Ver/Abrir |