Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 141, pp. 1-12.

Title: Behavior of the maximal solution of the Cauchy problem for some
       nonlinear pseudoparabolic equation as $|x|\to\infty$ 

Author: Tatiana Kavitova (Vitebsk State Univ., Belarus)

Abstract:
 We prove a comparison principle for solutions of the Cauchy problem of the
 nonlinear pseudoparabolic equation $u_t=\Delta u_t+ \Delta\varphi(u) +h(t,u)$
 with nonnegative bounded initial data.
 We show stabilization of a maximal solution to a maximal solution of
 the Cauchy problem for the corresponding ordinary differential
 equation $\vartheta'(t)=h(t,\vartheta)$ as $|x|\to\infty$ under certain
 conditions on an initial datum.

Submitted March 22, 2012. Published August 20, 2012.
Math Subject Classifications: 35B40, 35B51, 35K70.
Key Words: Pseudoparabolic equation; comparison principle; stabilization.