Publicação
Asymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equation
| Resumo: | We consider the initial value problem (IVP) associated to the modified Zakharov-Kuznetsov (mZK) equation \begin{equation}\nonumber u_t+6u^2u_x+u_{xxx}+u_{xyy}=0, \quad (x,y)\in \mathbb{R}^2, \; t \in \mathbb{R}, \end{equation} which is known to have global solution for given data in $u(x,y,0) = u_0(x,y)\in H^1(\mathbb{R}^2)$ satisfying $\|u_0\|_{L^2} <\sqrt{3} \|\phi\|_{L^2}$, where $\phi$ is a solitary wave solution. In this work, the issue of the asymptotic behavior of the solutions of the modified Zakharov-Kuznetsov equation with negative energy is addressed. The principal tool to obtain the main result is the use of appropriate scaling argument from Angulo et al [4, 5]. |
|---|---|
| Autores principais: | Panthee, Mahendra |
| Outros Autores: | Scialom, Marcia |
| Assunto: | Dispersive equation KdV equation Blow-up solution |
| Ano: | 2010 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | We consider the initial value problem (IVP) associated to the modified Zakharov-Kuznetsov (mZK) equation \begin{equation}\nonumber u_t+6u^2u_x+u_{xxx}+u_{xyy}=0, \quad (x,y)\in \mathbb{R}^2, \; t \in \mathbb{R}, \end{equation} which is known to have global solution for given data in $u(x,y,0) = u_0(x,y)\in H^1(\mathbb{R}^2)$ satisfying $\|u_0\|_{L^2} <\sqrt{3} \|\phi\|_{L^2}$, where $\phi$ is a solitary wave solution. In this work, the issue of the asymptotic behavior of the solutions of the modified Zakharov-Kuznetsov equation with negative energy is addressed. The principal tool to obtain the main result is the use of appropriate scaling argument from Angulo et al [4, 5]. |
|---|