Carleman Estimates and Controllability of Stochastic degenerate parabolic Heat Equations

TL;DR

This paper develops new Carleman estimates to analyze the null controllability of stochastic degenerate parabolic heat equations, advancing control theory for such complex stochastic systems.

Contribution

It introduces novel Carleman estimates for stochastic degenerate equations and demonstrates their application in establishing null controllability results.

Findings

Global Carleman estimate for stochastic degenerate equations established

Null controllability proved for backward stochastic equations

Partial controllability results obtained for forward equations

Abstract

This paper concerns the null controllability for a class of stochastic degenerate parabolic equations. We first establish a global Carleman estimate for a linear forward stochastic degenerate equation with multiplicative noise. Using this estimate we prove the null controllability of the backward equation and obtain a partial result for the controllability of the forward equation. Also, using a new Carleman estimate for backward equation with weighted function which does not vanish at time t = 0 and the duality method HUM we get the null controllability of a forward stochastic degenerate equation under the action of two controls.