Large deviations for stochastic porous media equation on general measure spaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Wu, Weina¹  Zhai, Jianliang² 

[1] Nanjing Univ Finance & Econ, Sch Econ, Nanjing 210023, Jiangsu, Peoples R China

[2] Univ Sci & Technol China, Sch Math Sci, CAS Wu Wen Tsun Key Lab Math, Hefei 230026, Anhui, Peoples R China

关键词: Porous media equation;    Sub-Markovian;    Strongly continuous contraction semigroup;    Weak convergence method;    Large deviations;   

DOI  :  10.1016/j.jde.2020.07.003

来源: Elsevier

【 摘 要 】

In this paper, we establish a large deviation principle for stochastic porous media equations driven by time-dependent multiplicative noise on a sigma-finite measure space (E, B(E), mu), and with the Laplacian replaced by a negative definite self-adjoint operator. The coefficient Psi is only assumed to satisfy the increasing Lipschitz nonlinearity assumption without the restriction r Psi (r) -> infinity as r -> infinity for L-2(mu)-initial data. This paper also gets rid of the compact embedding assumption on the associated Gelfand triple. Examples of the negative definite self-adjoint operators include fractional powers of the Laplacian, i.e. L = -(-Delta)(alpha), alpha is an element of (0, 1], generalized Schrodinger operators, i.e. L = Delta + 2 del rho/rho. del, and Laplacians on fractals. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free