Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:495

Article

关键词: Stochastic partial differential equation;    SPDE;    Existence and uniqueness;    Mild solution;    Numerical approximation;    Weak approximation;   

DOI  :  10.1016/j.jmaa.2020.124558

来源: Elsevier

【 摘 要 】

In this article we develop a framework for studying parabolic semilinear stochastic evolution equations (SEEs) with singularities in the initial condition and singularities at the initial time of the time-dependent coefficients of the considered SEE. We use this framework to establish existence, uniqueness, and regularity results for mild solutions of parabolic semilinear SEEs with singularities at the initial time. We also provide several counterexample SEEs that illustrate the optimality of our results. (C) 2020 Published by Elsevier Inc.

【 授权许可】

Free