Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 109, pp. 1-11.
Title: Initial-boundary value problems for nonlinear pseudoparabolic
equations in a critical case
Author: Elena I. Kaikina (Univ. Nacional Autonoma de Mexico, Morelia, Mexico)
Abstract:
We study nonlinear pseudoparabolic equations, on the half-line
in a critical case,
$\displaylines{
\partial _{t}( u-u_{xx}) -\alpha u_{xx}=\lambda |u| u,\quad
x\in \mathbb{R}^{+},\; t>0, \cr
u( 0,x) =u_{0}( x) , \quad x\in \mathbb{R}^{+}, \cr
u(t,0)=0,
}$$
where $\alpha >0$, $\lambda \in \mathbb{R}$.
The aim of this paper is to prove the existence of global solutions
to the initial-boundary value problem and to find the main term
of the asymptotic representation of solutions.
Submitted March 22, 2007. Published August 7, 2007.
Math Subject Classifications: 35Q35
Key Words: Dissipative nonlinear evolution equation; Sobolev equation;
large time asymptotic behavior.