Null controllability for stochastic parabolic equations with Robin boundary conditions

TL;DR

This paper proves the null controllability of stochastic parabolic equations with Robin boundary conditions using novel Carleman estimates in negative Sobolev spaces, advancing control theory for stochastic PDEs.

Contribution

It introduces new global Carleman estimates for stochastic parabolic equations with Robin boundary conditions, enabling null controllability results.

Findings

Established null controllability for stochastic parabolic equations with Robin boundary conditions.

Derived two new Carleman estimates in negative Sobolev spaces for the adjoint equations.

Applied duality method to prove controllability results.

Abstract

We establish the null controllability of forward and backward linear stochastic parabolic equations with linear Robin (or Fourier) boundary conditions. These equations incorporate zero and first order terms with bounded coefficients. To prove our null controllability results, a key tool will be the derivation of two new global Carleman estimates for the weak solutions of the corresponding adjoint equations in negative Sobolev space. These Carleman estimates are established using a duality method.