Insensitizing controls for stochastic parabolic equations with dynamic boundary conditions

TL;DR

This paper investigates controllability of stochastic heat equations with dynamic boundary conditions, introducing a control approach that simplifies previous models and establishing key observability and controllability results.

Contribution

It presents a novel control method for stochastic heat equations with dynamic boundary conditions using only one control and spectral inequalities.

Findings

Established observability inequality for the adjoint system

Proved null controllability of the stochastic heat equation

Achieved approximate controllability under new conditions

Abstract

In this paper, we continue the study of some controllability issues for the forward stochastic heat equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra forces in the noise parts. Under a strong measurability condition, and using a spectral inequality, we first establish an appropriate observability inequality for the corresponding adjoint system. Then, by the classical duality approach, the null and approximate controllability results are established.