Carleman and observability estimates for stochastic beam equation

TL;DR

This paper develops Carleman and observability estimates for the stochastic beam equation using multiplier and cutoff techniques, providing new tools for control and analysis of such stochastic systems.

Contribution

It introduces a novel weight identity and establishes the first global Carleman estimate for the stochastic beam equation, leading to boundary observability results.

Findings

Established a weight identity for stochastic beam equations

Derived a global Carleman estimate for the system

Obtained boundary observability estimates

Abstract

In this paper, we establish a weight identity for stochastic beam equation by means of the multiplier method. Based on this identity, we first establish the global Carleman estimate for the special system with zero initial value and end value, then a revised Carleman estimate for stochastic beam equation is established through a cutoff technique. Finally, we use the revised Carleman estimate to get the required boundary observability estimate.