Optimal control for stochastic heat equation with memory

TL;DR

This paper studies the existence and uniqueness of solutions for stochastic heat equations with memory and explores an optimal control problem where control and noise influence the system simultaneously.

Contribution

It establishes foundational results for stochastic heat equations with memory and introduces an optimal control framework involving noise and control interactions.

Findings

Proved existence and uniqueness of solutions for the stochastic heat equation with memory.

Formulated and analyzed an optimal control problem for the system.

Provided insights into control strategies in noisy heat conduction models.

Abstract

In this paper, we investigate the existence and uniqueness of solutions for a class of evolutionary integral equations perturbed by a noise arising in the theory of heat conduction. As a motivation of our results, we study an optimal control problem when the control enters the system together with the noise.