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Random attractor for the reaction-diffusion equation perturbed by a stochastic càdlàg process
Author(s):
O.
V.
Kapustyan;
J.
Valero;
O.
V.
Pereguda
Translated by:
S. Kvasko
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 73
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 73
(2006),
57-69.
MSC (2000):
Primary 34F05, 60H10
Posted:
January 17, 2007
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Additional information
Abstract:
We study a stochastically perturbed reaction-diffusion equation by using the methods of the theory of stochastic attractors. It is proved that solutions of the equation form a multivalued random dynamic system for which there exists a random attractor in the phase space.
References:
-
- 1.
- L. Arnold, Random Dynamical Systems, Springer, Berlin, 1998. MR 1723992 (2000m:37087)
- 2.
- I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes, ``Nauka'', Moscow, 1977; English transl. of the first edition, Scripta Technica, Inc. W. B. Saunders Co., Philadelphia, Pa.-London-Toronto, Ont., 1969. MR 0488196 (58:7758)
- 3.
- A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, ``Nauka'', Moscow, 1989; English transl., North-Holland Publishing Co., Amsterdam, 1992. MR 1007829 (92f:58101)
- 4.
- A. V. Kapustyan, Global attractors of a nonautonomous reaction-diffusion equation, Differ. Uravn. 38 (2002), no. 10, 1378-1382; English transl. in Differ. Equ. 38 (2002), no. 10, 1467-1471. MR 1984456 (2004g:35028)
- 5.
- H. Crauel and F. Flandoli, Attractors for random dynamical systems, Probab. Theory Related Fields 100 (1994), 365-393. MR 1305587 (95k:58092)
- 6.
- H. Crauel, Global random attractors are uniquely determined by attracting deterministic compact sets, Ann. Mat. Pura Appl. 126 (1999), no. 4, 57-72. MR 1746535 (2000m:37090)
- 7.
- K. R. Schenk-Hoppe, Random attractors--general properties, existence and applications to stochastic bifurcation theory, Discrete Contin. Dyn. Syst. 4 (1998), no. 1, 99-130. MR 1485366 (98h:34103)
- 8.
- T. Caraballo, J. A. Langa, and J. Valero, Global attractors for multivalued random dynamical systems, Nonlinear Anal. 48 (2002), 805-829. MR 1878338 (2003a:37068)
- 9.
- J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, 1990. MR 1048347 (91d:49001)
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Additional Information:
O.
V.
Kapustyan
Affiliation:
Department of Integral and Differential Equations, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
alexkap@univ.kiev.ua
J.
Valero
Affiliation:
Universidad Miguel Hernandez, Centro de Investigation Operativa, Avda. del ferrocarril s/n 03202 Elche (Alicante), Spain
Email:
jvalero@umh.es
O.
V.
Pereguda
Affiliation:
Department of Integral and Differential Equations, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
perol@ua.fm
DOI:
10.1090/S0094-9000-07-00681-3
PII:
S 0094-9000(07)00681-3
Received by editor(s):
24/AUG/2004
Posted:
January 17, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
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