Global Carleman estimates for linear stochastic Kawahara equation and their applications

被引：10

作者：

Gao, Peng ^{[1
]}

机构：

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

来源：

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS | 2016年 / 28卷 / 03期

关键词：

linear stochastic Kawahara equation; Carleman estimate; unique continuation property; SCHRODINGER-EQUATIONS; EXACT CONTROLLABILITY; NULL CONTROLLABILITY; PARABOLIC EQUATIONS; BOUNDED DOMAIN;

D O I：

10.1007/s00498-016-0173-6

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this study, we first establish an identity for a stochastic fifth-order Kawahara operator, and then, applying this identity, weobtain two global Carleman estimates for linear stochastic Kawahara equation. Based on these estimates, we obtain two types of unique continuation property for linear stochastic Kawahara equation.

引用

页数：22

共 23 条

[11]

Korteweg D J., 1895, PHILOS MAG, V5, P422, DOI [10.1080/14786449508620739, DOI 10.1080/14786449508620739]

[12] Modified KdV equation with a source term in a bounded domain [J].

Larkin, NA .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2006, 29 (07) :751-765

[13]

Lions J. L., 1972, Non-Homogeneous Boundary-Value Problems and Applications

[14] GLOBAL CARLEMAN ESTIMATE FOR STOCHASTIC PARABOLIC EQUATIONS, AND ITS APPLICATION [J].

Liu, Xu .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2014, 20 (03) :823-839

[15] EXACT CONTROLLABILITY FOR STOCHASTIC TRANSPORT EQUATIONS [J].

Lu, Qi .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2014, 52 (01) :397-419

[16] Exact controllability for stochastic Schrodinger equations [J].

Lu, Qi .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (08) :2484-2504

[17] OBSERVABILITY ESTIMATE FOR STOCHASTIC SCHRODINGER EQUATIONS AND ITS APPLICATIONS [J].

Lu, Qi .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2013, 51 (01) :121-144

[18] Carleman estimate for stochastic parabolic equations and inverse stochastic parabolic problems [J].

Lu, Qi .

INVERSE PROBLEMS, 2012, 28 (04)

[19]

Renardy M., 2004, An Introduction to Partial Differential Equations, V2nd edn

[20] NULL CONTROLLABILITY FOR FORWARD AND BACKWARD STOCHASTIC PARABOLIC EQUATIONS [J].

Tang, Shanjian ;

Zhang, Xu .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (04) :2191-2216

← 1 2 3 →