Behavior of the maximal solution of the Cauchy problem for some nonlinear pseudoparabolic equation as $|x|oinfty$
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 correspondi...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2012-08-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/141/abstr.html |
| Summary: | 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. |
|---|---|
| ISSN: | 1072-6691 |