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.