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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
Volume: 118
Issue: 4
Year: 1993
Pages: 401-423
Summary lang: English
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Category: math
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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
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Date available: 2009-09-24T21:01:39Z
Last updated: 2015-08-30
Stable URL: http://hdl.handle.net/10338.dmlcz/126159
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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
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