Exact controllability for some degenerate wave equations

被引：10

作者：

Bai, Jinyan ^{[1
,2
]}

Chai, Shugen ^{[1
]}

机构：

[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Peoples R China

[2] Jinzhong Univ, Sch Math, Jinzhong 030619, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2020年 / 43卷 / 12期

基金：

中国国家自然科学基金;

关键词：

boundary control; controllability; degenerate wave equation; observability; NULL CONTROLLABILITY; PARABOLIC EQUATIONS;

D O I：

10.1002/mma.6464

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study one-dimensional linear degenerate wave equations with a distributed controller. We establish observability inequalities for degenerate wave equation by multiplier method. We also deduce the exact controllability for degenerate wave equation by Hilbert uniqueness method when the control acts on the nondegenerate boundary. Moreover, an explicit expression for the controllability time is given.

引用

页码：7292 / 7302

页数：11

共 16 条

[1] Carleman estimates for degenerate parabolic operators with applications to null controllability [J].

Alabau-Boussouira, F. ;

Cannarsa, P. ;

Fragnelli, G. .

JOURNAL OF EVOLUTION EQUATIONS, 2006, 6 (02) :161-204

[2] CONTROL AND STABILIZATION OF DEGENERATE WAVE EQUATIONS [J].

Alabau-Boussouira, Fatiha ;

Cannarsa, Piermarco ;

Leugering, Guenter .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2017, 55 (03) :2052-2087

[3]

Brown TS., 2018, APPL MATH NONLINEAR, V3, P55, DOI DOI 10.21042/AMNS.2018.1.00006

[4] Carleman estimates for a class of degenerate parabolic operators [J].

Cannarsa, P. ;

Martinez, P. ;

Vancostenoble, J. .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2008, 47 (01) :1-19

[5]

Cannarsa P, 2005, ADV DIFFERENTIAL EQU, V10, P153

[6] Carleman estimates and null controllability for boundary-degenerate parabolic operators [J].

Cannarsa, Piermarco ;

Martinez, Partick ;

Vancostenoble, Judith .

COMPTES RENDUS MATHEMATIQUE, 2009, 347 (3-4) :147-152

[7]

Citti G., 2004, Commun. Appl. Anal., V8, P125

[8] Null controllability for a class of degenerate parabolic equations with the gradient terms [J].

Du, Runmei .

JOURNAL OF EVOLUTION EQUATIONS, 2019, 19 (02) :585-613

[9] FLEMING-VIOT PROCESSES IN POPULATION-GENETICS [J].

ETHIER, SN ;

KURTZ, TG .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1993, 31 (02) :345-386

[10] EXACT BOUNDARY CONTROLLABILITY OF 1-D PARABOLIC AND HYPERBOLIC DEGENERATE EQUATIONS [J].

Gueye, Mamadou .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2014, 52 (04) :2037-2054

← 1 2 →