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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:
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