Large deviations for stochastic porous media equation on general measure spaces

[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.

[发布日期] 2020-11-15

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