Null controllability for a class of stochastic singular parabolic equations with the convection term

Lin Yan; Bin Wu

doi:10.3934/dcdsb.2021182

Article Contents

2022, Volume 27, Issue 6: 3213-3240. Doi: 10.3934/dcdsb.2021182

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Null controllability for a class of stochastic singular parabolic equations with the convection term

Lin Yan and
Bin Wu^,

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

^* Corresponding author: Bin Wu
^* Corresponding author: Bin Wu

Received: August 31, 2020

Revised: April 30, 2021

Published: June 2022

This work is supported by NSFC (No.11661004, No.11601240)

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Abstract

This paper concerns the null controllability for a class of stochastic singular parabolic equations with the convection term in one dimensional space. Due to the singularity, we first transfer to study an approximate nonsingular system. Next we establish a new Carleman estimate for the backward stochastic singular parabolic equation with convection term and then an observability inequality for the adjoint system of the approximate system. Based on this observability inequality and an approximate argument, we obtain the null controllability result.

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Mathematics Subject Classification: 93B05, 93B07, 35R60, 35K67.

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