A semigroup approach to stochastic systems with input delay at the boundary

S. Hadd; F.Z. Lahbiri

doi:10.3934/mcrf.2022004

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2023, Volume 13, Issue 2: 454-469. Doi: 10.3934/mcrf.2022004

This issue Previous Article Next Article Carleman estimates for a magnetohydrodynamics system and application to inverse source problems

A semigroup approach to stochastic systems with input delay at the boundary

S. Hadd^, and
F.Z. Lahbiri

Department of Mathematics, Faculty of Sciences Agadir, Ibn Zohr University, Hay Dakhla, BP. 8106, 80000–Agadir, Morocco

^* Corresponding author: S. Hadd, s.hadd@uiz.ac.ma
^* Corresponding author: S. Hadd, s.hadd@uiz.ac.ma

Received: July 2021

Revised: December 2021

Early access: February 2022

Published: June 2023

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Abstract

This work focuses on the well-posedness of abstract stochastic linear systems with boundary input delay and unbounded observation operators. We use product spaces and a semigroup approach to reformulate such delay systems into free-delay distributed stochastic systems with unbounded control and observation operators. This gives us the opportunity to use the concept of admissible control and observation operators as well as the concept of Yosida extensions to prove the existence and uniqueness of the solution process and provide an estimation of the observation process in relation to initial conditions and control process. As an example, we consider a stochastic Schrödinger system with input delay.

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Mathematics Subject Classification: Primary: 93E03, 93C23; Secondary: 93B28.

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