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.