Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 89, pp. 1-16.

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

Authors: Rosa E. Cardiel  (UNAM, Campus Cuernavaca, Mexico)
         Elena I. Kaikina (UNAM, Campus Morelia,  Mexico)
	 
Abstract: 
 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.

Submitted February 10, 2006. Published August 9, 2006.
Math Subject Classifications: 35Q35, 35B40.
Key Words: Pseudodifferential operator; large data; asymptotic behavior.