Stochastic parabolic evolution equations in M-type 2 Banach spaces

TL;DR

This paper investigates stochastic parabolic evolution equations with additive noise in M-type 2 Banach spaces, establishing existence, uniqueness, and regularity of solutions for both linear and semilinear cases, with applications to SPDEs.

Contribution

It provides a comprehensive analysis of strict and mild solutions, including their regularities and dependence on initial data, in the context of M-type 2 Banach spaces, which is a novel setting.

Findings

Existence and uniqueness of solutions in linear and semilinear cases.

Maximal regularity results for strict and mild solutions.

Regular dependence of solutions on initial data.

Abstract

This paper is devoted to studying stochastic parabolic evolution equations with additive noise in Banach spaces of M-type 2. We construct both strict and mild solutions possessing very strong regularities. First, we consider the linear case. We prove existence and uniqueness of strict and mild solutions and show their maximal regularities. Second, we explore the semilinear case. Existence, uniqueness and regularity of mild and strict solutions are shown. Regular dependence of mild solutions on initial data is also investigated. Finally, some applications to stochastic partial differential equations are presented.