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Invariant measures of fractional stochastic delay reaction–diffusion equations on unbounded domains.
- Source :
-
Nonlinearity . Jun2021, Vol. 34 Issue 6, p1-48. 48p. - Publication Year :
- 2021
-
Abstract
- In this paper, existence of invariant measure is mainly investigated for a fractional stochastic delay reaction–diffusion equation defined on unbounded domains. We first establish the mean-square uniform smallness of the tails of the solutions in order to overcome the non-compactness of standard Sobolev embeddings on unbounded domains. We then show the weak compactness of a family of probability distributions of the solutions by combining the Ascoli–Arzelŕ theorem, the uniform tail-estimates as well as the technique of dyadic division. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09517715
- Volume :
- 34
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Nonlinearity
- Publication Type :
- Academic Journal
- Accession number :
- 151087559
- Full Text :
- https://doi.org/10.1088/1361-6544/ac0125