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

TL;DR

This paper investigates the existence and uniqueness of solutions for stochastic parabolic equations with boundary white noise using integrated semigroup theory, extending the analysis to non-dense domains and non-homogeneous boundary conditions.

Contribution

It introduces an integrated semigroup approach to handle stochastic evolution equations with boundary white noise and non-dense domains, providing new existence and uniqueness results.

Findings

Established existence and uniqueness of mild solutions

Applied results to stochastic parabolic equations with Neumann boundary conditions

Extended analysis to non-sectorial operators and non-dense domains

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.