Existence results for linear evolution equations of parabolic type

2015/05/06 by Tôn Việt Tạ, Ta, Ton Viet · 3 citations
Engineering · Mathematics · #35R60 #60H15 #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Probability (math.PR) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1505.01252

openalex publication_date 2015/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study both strict and mild solutions to parabolic evolution equations of the form dX+AXdt=F(t)dt+G(t)dW(t) in Banach spaces. First, we explore the deterministic case. The maximal regularity of solutions has been shown. Second, we investigate the stochastic case. We prove existence of strict solutions and show their space-time regularity. Finally, we apply our abstract results to a stochastic heat equation.

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