Behavior of the maximal solution of the Cauchy problem for some nonlinear pseudoparabolic equation as $|x|oinfty$

Abstract

We prove a comparison principle for solutions of the Cauchy problem of the nonlinear pseudoparabolic equation $u_t=Delta u_t+ Deltavarphi(u) +h(t,u)$ 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 $|x|oinfty$ under certain conditions on an initial datum.

Keywords

• Pseudoparabolic equation
• comparison principle
• stabilization