Nonlinear pseudodifferential equations on a half-line with large initial data

Cardiel, Rosa E. ; Kaikina, Elena I.

Electronic Journal of Differential Equations, Tome 2006 (2006).

Résumé

Summary: We study the initial-boundary value problem for nonlinear pseudodifferential equations, on a half-line, $$\displaylines{ u_{t}+\mathcal{\lambda}| u| ^{\sigma}u+\mathcal{L} u=0,\quad(x,t)\in{\mathbb{R}^{+}}\times{\mathbb{R}^{+}},\cr u(x,0)=u_{0}(x),\quad x\in{\mathbb{R}}^{+}, }$$ where $\lambda>0$ and pseudodifferential operator $\mathcal{L}$ is defined by the inverse Laplace transform. The aim of this paper is to prove the global existence of solutions and to find the main term of the asymptotic representation in the case of the large initial data.

Détail

Classification : 35Q35, 35B40
Keywords: pseudodifferential operator, large data, asymptotic behavior