Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

 
 

 

Random attractor for the reaction-diffusion equation perturbed by a stochastic càdlàg process


Authors: O. V. Kapustyan, J. Valero and O. V. Pereguda
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 73 (2005).
Journal: Theor. Probability and Math. Statist. 73 (2006), 57-69
MSC (2000): Primary 34F05, 60H10
DOI: https://doi.org/10.1090/S0094-9000-07-00681-3
Published electronically: January 17, 2007
MathSciNet review: 2213841
Full-text PDF Free Access

Abstract | References | Similar Articles | 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 [Enhancements On Off] (What's this?)

  • 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)

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 34F05, 60H10

Retrieve articles in all journals with MSC (2000): 34F05, 60H10


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: https://doi.org/10.1090/S0094-9000-07-00681-3
Received by editor(s): August 24, 2004
Published electronically: January 17, 2007
Article copyright: © Copyright 2007 American Mathematical Society

American Mathematical Society