期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
卷 27, 期 5, 页码 2483-2499出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdsb.2021142
关键词
stochastic evolution equation; random dynamical systems; center manifolds; exponential trichotomy; integrated semigroup
资金
- National Natural Science Foundation of China [11871225]
- Guangdong Basic and Applied Basic Research Foundation [:2019A1515011350]
The aim of this paper is to develop a center manifold theory for a class of stochastic partial differential equations with a non-dense domain using the Lyapunov-Perron method and the resolvent operator to construct a novel variation of constants formula. An additional condition involving a non-decreasing map is imposed to deduce the required estimate, as Young's convolution inequality is not applicable. As an application, a stochastic parabolic equation is presented to illustrate the obtained results.
The aim of this paper is to develop a center manifold theory for a class of stochastic partial differential equations with a non-dense domain through the Lyapunov-Perron method. We construct a novel variation of constants formula by the resolvent operator to formulate the integrated solutions. Moreover, we impose an additional condition involving a non-decreasing map to deduce the required estimate since Young's convolution inequality is not applicable. As an application, we present a stochastic parabolic equation to illustrate the obtained results.
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