2015/08/28 by Tôn Việt Tạ, Ta, Ton Viet
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1508.07340
openalex publication_date 2015/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.