| Title:
|
A dynamical system in a Hilbert space with a weakly attractive nonstationary point (English) |
| Author:
|
Vrkoč, Ivo |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
118 |
| Issue:
|
4 |
| Year:
|
1993 |
| Pages:
|
401-423 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A differential equation is a Hilbert space with all solutions bounded but with so finite nontrivial invariant measure is constructed. In fact, it is shown that all solutions to this equation converge weakly to the origin, nonetheless, there is no stationary point. Moreover, so solution has a non-empty $\Omega$-set. (English) |
| Keyword:
|
invariant measures |
| Keyword:
|
stochastic evolution equations |
| Keyword:
|
Hilbert space |
| Keyword:
|
compact semigroup |
| Keyword:
|
Galerkin approximation |
| Keyword:
|
differential equations in Hilbert spaces |
| Keyword:
|
$\Omega$-sets |
| MSC:
|
34D99 |
| MSC:
|
34F05 |
| MSC:
|
34G20 |
| MSC:
|
60H15 |
| idZBL:
|
Zbl 0794.34054 |
| idMR:
|
MR1251884 |
| DOI:
|
10.21136/MB.1993.126159 |
| . |
| Date available:
|
2009-09-24T21:01:39Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126159 |
| . |
| Reference:
|
[1] G. Da Prato D. Gątarek J. Zabczyk: Invariant measures for semilinear stochastic equations.Stochastic Anal. Appl. 10 (1992), 387-408. MR 1178482, 10.1080/07362999208809278 |
| Reference:
|
[2] N. N. Vakhaniya V. I. Tarieladze S. A. Chobanyan: Probability distributions in Banach spaces.Nauka, Moscow, 1985. (In Russian.) MR 0787803 |
| . |
