Semilinear stochastic equations with bilinear fractional noise
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60461373%3A22340%2F16%3A43902582" target="_blank" >RIV/60461373:22340/16:43902582 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/16:10330467
Result on the web
<a href="http://dx.doi.org/10.3934/dcdsb.2016088" target="_blank" >http://dx.doi.org/10.3934/dcdsb.2016088</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcdsb.2016088" target="_blank" >10.3934/dcdsb.2016088</a>
Alternative languages
Result language
angličtina
Original language name
Semilinear stochastic equations with bilinear fractional noise
Original language description
In the paper, we study existence and uniqueness of solutions to semilinear stochastic evolution systems, driven by a fractional Brownian motion with bilinear noise term, and the long time behavior of solutions to such equations. For this purpose, we study at first the random evolution operator defined by the corresponding bilinear equation which is later used to define the mild solution of the semilinear equation. The mild solution is also shown to be weak in the PDE sense. Furthermore, the asymptotic behavior is investigated by using the Random Dynamical Systems theory. We show that the solution generates a random dynamical system that, under appropriate stability and compactness conditions, possesses a random attractor. ? 2016, Southwest Missouri State University. All rights reserved.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA15-08819S" target="_blank" >GA15-08819S: Stochastic Processes in Infinite Dimensional Spaces</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete and Continuous Dynamical Systems - Series B
ISSN
1531-3492
e-ISSN
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Volume of the periodical
21
Issue of the periodical within the volume
9
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
3075-3094
UT code for WoS article
000388953300010
EID of the result in the Scopus database
2-s2.0-84992650937