Abstract Parabolic Equations with boundary white noise: an integrated semigroup approach

2023/07/23 by Arnaud Ducrot, Ducrot, Arnaud, Fatima Zahra Lahbiri +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2307.12294

openalex publication_date 2023/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the existence of solution for stochastic evolution equations with almost sectorial operators and possibly a non dense domain. Such problems cover several types of evolution equations, we are interested here in particular in evolution equations with non-homogenous boundary conditions of white noise type. We obtain the existence and uniqueness of mild solutions in state space using the integrated semigroup theory. The results are applied to stochastic parabolic equations with Neumann boundary conditions.

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