Global Carleman estimates for the linear stochastic Kuramoto-Sivashinsky equations and their applications

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Gao, Peng^1,2 

[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China

[2] Northeast Normal Univ, Ctr Math & Interdisciplinary Sci, Changchun 130024, Jilin, Peoples R China

关键词: Stochastic Kuramoto Sivashinsky equation;    Carleman estimate;    Observability;    Null controllability;    Unique continuation property;   

DOI  :  10.1016/j.jmaa.2018.04.033

来源: Elsevier

【 摘 要 】

In this paper, we establish two new global Carleman estimates for the linear stochastic Kuramoto-Sivashinsky equations. The first one is for the backward linear stochastic Kuramoto-Sivashinsky equation. Based on this estimate and the duality argument, we obtain the null controllability of the forward linear stochastic Kuramoto-Sivashinsky equation by three controls, one is an internal control in the diffusion term and the others are boundary controls. The second one is for the forward linear stochastic Kuramoto-Sivashinsky equation. According to this estimate, we obtain a unique continuation property for the forward linear stochastic Kuramoto-Sivashinsky equation. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free