Carleman Estimates and Controllability of Stochastic degenerate parabolic Heat Equations

2022/02/21 by M. Baroun, M. Fadili, Baroun, M. +5
Computer Science · Engineering · Mathematics · #35K65 #93B07 #93E99 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Primary 60H15 #Secondary 93B05 #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2202.10070

openalex publication_date 2022/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Null Controllability for Stochastic Parabolic Equations with convection terms
• Carleman Estimates and Controllability of Forward Stochastic Parabolic Equations with General Dynamic Boundary Conditions
• Null Controllability for Backward Stochastic Parabolic Convection-Diffusion Equations with Dynamic Boundary Conditions
• New global Carleman estimates and null controllability for forward/backward semi-linear parabolic SPDEs
• New global Carleman estimates and null controllability for a stochastic Cahn-Hilliard type equation