Nonlinear stochastic time-fractional slow and fast diffusion equations on Rd

[摘要] This paper studies the nonlinear stochastic partial differential equation of fractional orders both in space and time variables: (partial derivative(beta) + nu/2(-Delta)(alpha/2))u(t, x) = I-t(gamma) [rho(u(t, x))W(t, x)], t > 0, x is an element of R-d. where W is the space-time white noise, alpha is an element of (0, 2], beta is an element of (0, 2), gamma >= 0 and nu > 0. Fundamental solutions and their properties, in particular the nonnegativity, are derived. The existence and uniqueness of solution together with the moment bounds of the solution are obtained under Dalangs condition: d < 2 alpha + alpha/beta min (2 gamma -1, 0). In some cases, the initial data can be measures. When beta is an element of (0, 1], we prove the sample path regularity of the solution. (C) 2019 Elsevier B.V. All rights reserved.

[发布日期] 2019-12-01

[关键词] Nonlinear stochastic fractional diffusion equations;Measure-valued initial data;Holder continuity;Intermittency;The Fox H-function