Unique continuation property for stochastic nonclassical diffusion equations and stochastic linearized Benjamin-Bona-Mahony equations

Peng Gao

doi:10.3934/dcdsb.2018262

Article Contents

2019, Volume 24, Issue 6: 2493-2510. Doi: 10.3934/dcdsb.2018262

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Unique continuation property for stochastic nonclassical diffusion equations and stochastic linearized Benjamin-Bona-Mahony equations

Peng Gao^,

School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, China

* Corresponding author: Peng Gao
* Corresponding author: Peng Gao

Received: November 2017

Revised: May 2018

Early access: October 2018

Published: June 2019

The author is supported by NSFC Grant (11601073) and NSFC Grant (11701078)

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Abstract

In this paper, we first establish two global Carleman estimates for linear stochastic nonclassical diffusion equations. Based on these estimates, we obtain two types of Unique Continuation Property for stochastic nonclassical diffusion equations and stochastic linearized Benjamin-Bona-Mahony equations.

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Mathematics Subject Classification: Primary: 35Q53; Secondary: 60H15.

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References

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