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Higher-order Wong–Zakai approximations of stochastic reaction–diffusion equations on [formula omitted].
- Source :
-
Physica D . Jan2020, Vol. 401, pN.PAG-N.PAG. 1p. - Publication Year :
- 2020
-
Abstract
- In this paper, we consider the higher-order Wong–Zakai approximations of the non-autonomous stochastic reaction–diffusion equation driven by additive/multiplicative white noises. The solutions between the approximation equation and stochastic reaction–diffusion equation are compared in higher-order spaces, in terms of the initial data. Based on these results and the known L 2 -upper semi-continuity, we prove that the random attractor of the approximation random system converges to that of the non-autonomous stochastic reaction–diffusion equation with additive/multiplicative white noises in L p (R N) ∩ H 1 (R N) when the size of the approximation shrinks to zero. • Approximation is obtained in L p ∩ H 1 for equations with additive noise. • Approximation is obtained in L p ∩ H 1 for equations with multiplicative noises. • Upper semi-continuity w.r.t. the size of approximations is derived in L p ∩ H 1 . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01672789
- Volume :
- 401
- Database :
- Academic Search Index
- Journal :
- Physica D
- Publication Type :
- Academic Journal
- Accession number :
- 139766880
- Full Text :
- https://doi.org/10.1016/j.physd.2019.132147