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.