| Title:
|
The long-time behaviour of the solutions to semilinear stochastic partial differential equations on the whole space (English) |
| Author:
|
Manthey, Ralf |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
15-39 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Cauchy problem for a stochastic partial differential equation with a spatial correlated Gaussian noise is considered. The "drift" is continuous, one-sided linearily bounded and of at most polynomial growth while the "diffusion" is globally Lipschitz continuous. In the paper statements on existence and uniqueness of solutions, their pathwise spatial growth and on their ultimate boundedness as well as on asymptotical exponential stability in mean square in a certain Hilbert space of weighted functions are proved. (English) |
| Keyword:
|
nuclear and cylindrical noise |
| Keyword:
|
existence and uniqueness of the solution |
| Keyword:
|
spatial growth |
| Keyword:
|
ultimate boundedness |
| Keyword:
|
asymptotic mean square stability |
| Keyword:
|
Cauchy problem |
| MSC:
|
35B40 |
| MSC:
|
35R60 |
| MSC:
|
60H15 |
| idZBL:
|
Zbl 0982.60055 |
| idMR:
|
MR1825855 |
| DOI:
|
10.21136/MB.2001.133912 |
| . |
| Date available:
|
2009-09-24T21:46:52Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133912 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
[9] R. Manthey, T. Zausinger: Stochastic evolution equations in ${\mathbb{L}}^{2\nu }_{\rho }$.Stochastics Stochastics Rep. 66 (1999), 37–85. MR 1687799, 10.1080/17442509908834186 |
| Reference:
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[10] R. Marcus: Stochastic diffusion on an unbounded domain.Pacific J. Math. 84 (1979), 143–153. Zbl 0423.60056, MR 0559632, 10.2140/pjm.1979.84.143 |
| Reference:
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[11] R. I. Ovsepian, A. Pełczyński: On the existence of a fundamental total biorthogonal sequence in every separable Banach space and related constructions of uniformly bounded orthonormal systems in ${\mathbb{L}}^2$.Studia Mathematica 54 (1975), 149–159. MR 0394137, 10.4064/sm-54-2-149-159 |
| Reference:
|
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| . |
