# A dynamical system in a Hilbert space with a weakly attractive nonstationary point

Mathematica Bohemica (1993)

- Volume: 118, Issue: 4, page 401-423
- ISSN: 0862-7959

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topVrkoč, Ivo. "A dynamical system in a Hilbert space with a weakly attractive nonstationary point." Mathematica Bohemica 118.4 (1993): 401-423. <http://eudml.org/doc/29313>.

@article{Vrkoč1993,

abstract = {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.},

author = {Vrkoč, Ivo},

journal = {Mathematica Bohemica},

keywords = {invariant measures; stochastic evolution equations; Hilbert space; compact semigroup; Galerkin approximation; differential equations in Hilbert spaces; $\Omega $-sets; invariant measures; stochastic evolution equations; Hilbert space; compact semigroup; Galerkin approximation},

language = {eng},

number = {4},

pages = {401-423},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A dynamical system in a Hilbert space with a weakly attractive nonstationary point},

url = {http://eudml.org/doc/29313},

volume = {118},

year = {1993},

}

TY - JOUR

AU - Vrkoč, Ivo

TI - A dynamical system in a Hilbert space with a weakly attractive nonstationary point

JO - Mathematica Bohemica

PY - 1993

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 118

IS - 4

SP - 401

EP - 423

AB - 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.

LA - eng

KW - invariant measures; stochastic evolution equations; Hilbert space; compact semigroup; Galerkin approximation; differential equations in Hilbert spaces; $\Omega $-sets; invariant measures; stochastic evolution equations; Hilbert space; compact semigroup; Galerkin approximation

UR - http://eudml.org/doc/29313

ER -

## References

top- G. Da Prato D. Gątarek J. Zabczyk, 10.1080/07362999208809278, Stochastic Anal. Appl. 10 (1992), 387-408. (1992) MR1178482DOI10.1080/07362999208809278
- N. N. Vakhaniya V. I. Tarieladze S. A. Chobanyan, Probability distributions in Banach spaces, Nauka, Moscow, 1985. (In Russian.) (1985) MR0787803

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