Stabilization of the Nonlinear Elastodynamic System with a Boundary Dissipation

被引：0

作者：

Zhang Zhifei ^{[1
]}

Yao Pengfei ^{[1
]}

机构：

[1] Chinese Acad Sci, Key Lab Control & Syst, Acad Math & Syst Sci, Beijing 100080, Peoples R China

来源：

PROCEEDINGS OF THE 27TH CHINESE CONTROL CONFERENCE, VOL 2 | 2008年

关键词：

Nonlinear elastodynamic systems; Energy estimate; Dissipative boundary structure;

D O I：

10.1109/CHICC.2008.4604943

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider the existence of global solutions of the nonlinear elastodynamic system with a boundary dissipation structure when initial data are small. The medium material is assumed to be isotropic and hyperelastic. We show the existence of global smooth solutions. In particular, we obtain the exponential decay of the energy, which implies the exponential stabilization of the system by boundary feedback.

引用

页码：577 / 579

页数：3

共 50 条

[1] Boundary stabilization of the linear anisotropic elastodynamic system
Bey, R
Heminna, A
Lohéac, JP
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 333 (12): : 1083 - 1088
[2] Boundary stabilization of a linear elastodynamic system with variable coefficients
Bey, Rabah
Heminna, Amar
Loheac, Jean-Pierre
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2001,
[3] Global smooth solutions and stabilization of nonlinear elastodynamic systems with locally distributed dissipation
Zhang, Zhi-Fei
Yao, Peng-Fei
[J]. SYSTEMS & CONTROL LETTERS, 2009, 58 (07) : 491 - 498
[4] Boundary stabilization of the elastodynamic system in a plane polygonal domain.
Brossard, R
Lohéac, JP
[J]. COMPTES RENDUS MATHEMATIQUE, 2004, 338 (03) : 213 - 218
[5] Boundary stabilization of linear elastodynamic system.: A new Approach
Bey, R
Heminna, A
Lohéac, JP
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 330 (07): : 563 - 566
[6] BOUNDARY STABILIZATION OF LINEAR ELASTODYNAMIC SYSTEMS
LAGNESE, J
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1983, 21 (06) : 968 - 984
[7] On the stabilization of the Timoshenko system by a weak nonlinear dissipation
Messaoudi, Salim A.
Mustafa, Muhammad I.
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2009, 32 (04) : 454 - 469
[8] Stabilization of the elastodynamic equations with a degenerate locally distributed dissipation
Tebou, Louis
[J]. SYSTEMS & CONTROL LETTERS, 2007, 56 (7-8) : 538 - 545
[9] STABILIZATION OF WAVE AND PLATE-LIKE EQUATIONS WITH NONLINEAR DISSIPATION ON THE BOUNDARY
LASIECKA, I
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1989, 79 (02) : 340 - 381
[10] Exponential stabilization for porous elastic system with one boundary dissipation
Ramos A.J.A.
Júnior D.S.A.
Freitas M.M.
Santos M.J.D.
Santos A.R.
[J]. ANNALI DELL'UNIVERSITA' DI FERRARA, 2020, 66 (1) : 113 - 134

← 1 2 3 4 5 →