Abstract Parabolic Equations with boundary white noise: an integrated semigroup approach
Analysis of PDEs
2023-07-25 v1 Probability
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.
Keywords
Cite
@article{arxiv.2307.12294,
title = {Abstract Parabolic Equations with boundary white noise: an integrated semigroup approach},
author = {Arnaud Ducrot and Fatima Zahra Lahbiri},
journal= {arXiv preprint arXiv:2307.12294},
year = {2023}
}