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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
Published electronically: January 17, 2007
MathSciNet review: 2213841
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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.


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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: http://dx.doi.org/10.1090/S0094-9000-07-00681-3
PII: S 0094-9000(07)00681-3
Received by editor(s): August 24, 2004
Published electronically: January 17, 2007
Article copyright: © Copyright 2007 American Mathematical Society