Nonlinear damped Timoshenko systems with second sound-Global existence and exponential stability

被引：81

作者：

Messaoudi, Salim A. ^{[1
]}

Pokojovy, Michael ^{[2
]}

Said-Houari, Belkacem ^{[3
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi Arabia

[2] Univ Konstanz, Fachbereich Math & Stat, D-78457 Constance, Germany

[3] Univ Badji Mokhtar, Lab Math Appl, Annaba 23000, Algeria

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2009年 / 32卷 / 05期

关键词：

Timoshenko systems; thermoelasticity; second sound; exponential decay; nonlinearity; global existence; SMOOTH SOLUTIONS; THERMOELASTICITY; BEAM; STABILIZATION; FEEDBACK; ENERGY; DECAY;

D O I：

10.1002/mma.1049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider nonlinear thermoelastic systems of Timoshenko type in a one-dimensional bounded domain. The system has two dissipative mechanisms being present in the equation for transverse displacement and rotation angle-a frictional damping and a dissipation through hyperbolic heat conduction modelled by Cattaneo's law, respectively. The global existence of small, smooth solutions and the exponential stability in linear and nonlinear cases are established. Copyright (C) 2008 John Wiley & Sons, Ltd.

引用

页码：505 / 534

页数：30

共 27 条

[21] SLEMROD M, 1981, ARCH RATION MECH AN, V76, P97
[22] Stabilization of Timoshenko beam
Soufyane, A
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 328 (08): : 731 - 734
[23] SOUFYANE A, 2003, J DIFFER EQUATIONS, V29, P1
[24] ON THE EXISTENCE OF SMOOTH SOLUTIONS IN ONE-DIMENSIONAL NONLINEAR THERMOELASTICITY WITH 2ND SOUND
TARABEK, MA
[J]. QUARTERLY OF APPLIED MATHEMATICS, 1992, 50 (04) : 727 - 742
[25] A smoothing property of a hyperbolic system and boundary controllability
Taylor, SW
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 114 (01) : 23 - 40
[26] On the correction for shear of the differential equation for transverse vibrations of prismatic bars
Timoshenko, SP
[J]. PHILOSOPHICAL MAGAZINE, 1921, 41 (245): : 744 - 746
[27] Stabilization of Timoshenko beam by means of pointwise controls
Xu, GQ
Yung, SP
[J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2003, 9 (09) : 579 - 600

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