| Title:
|
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations (English) |
| Author:
|
Poláčik, P. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
301-310 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider three types of semilinear second order PDEs on a cylindrical domain $\Omega \times (0,\infty )$, where $\Omega $ is a bounded domain in ${{\mathbb{R}}}^N$, $N\ge 2$. Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of $\Omega \times (0,\infty )$ is reserved for time $t$, the third type is an elliptic equation with a singled out unbounded variable $t$. We discuss the asymptotic behavior, as $t\rightarrow \infty $, of solutions which are defined and bounded on $\Omega \times (0,\infty )$. (English) |
| Keyword:
|
parabolic equations |
| Keyword:
|
elliptic equations |
| Keyword:
|
hyperbolic equations |
| Keyword:
|
asymptotic behavior |
| Keyword:
|
center manifold |
| MSC:
|
35B40 |
| MSC:
|
35G20 |
| MSC:
|
35J25 |
| MSC:
|
35J60 |
| MSC:
|
35K55 |
| MSC:
|
35L70 |
| MSC:
|
37L05 |
| idZBL:
|
Zbl 1010.35009 |
| idMR:
|
MR1981535 |
| DOI:
|
10.21136/MB.2002.134162 |
| . |
| Date available:
|
2012-10-05T13:04:33Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134162 |
| . |
| Reference:
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