Global well-posedness and exponential stability results of a class of Bresse-Timoshenko-type systems with distributed delay term

被引：33

作者：

Choucha, Abdelbaki ^{[1
]}

Ouchenane, Djamel ^{[2
]}

Zennir, Khaled ^{[3
]}

Feng, Baowei ^{[4
]}

机构：

[1] Univ El Oued, Fac Exact Sci, Dept Math, El Oued, Algeria

[2] Amar Teledji Univ Laghouat, Lab Pure & Appl Math, Laghouat, Algeria

[3] Qassim Univ, Dept Math, Coll Arts & Sci, Buraydah, Saudi Arabia

[4] SouthWestern Univ Finance & Econ, Dept Econ Math, Chengdu 611130, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年 / 47卷 / 13期

基金：

中国国家自然科学基金;

关键词：

Bresse-Timoshenko-type systems; distributed delay term; exponential decay; STABILIZATION; BOUNDARY; EQUATION; BEAM; THERMOELASTICITY;

D O I：

10.1002/mma.6437

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a Bresse-Timoshenko-type system with distributed delay term. Under suitable assumptions, we establish the global well-posedness of the initial and boundary value problem by using the Faedo-Galerkin approximations and some energy estimates. By using the energy method, we show two exponential stability results for the system with delay in vertical displacement and in angular rotation, respectively. This extends earlier results in the literature.

引用

页码：10668 / 10693

页数：26

共 26 条

[1] APPLICATION OF THE KREIN METHOD FOR DETERMINATION OF NATURAL FREQUENCIES OF PERIODICALLY SUPPORTED BEAM BASED ON SIMPLIFIED BRESSE-TIMOSHENKO EQUATIONS [J].

ABRAMOVICH, H ;

ELISHAKOFF, I .

ACTA MECHANICA, 1987, 66 (1-4) :39-59

[2] The hypothesis of equal wave speeds for stabilization of Timoshenko beam is not necessary anymore: the time delay cases [J].

Almeida Junior, D. S. ;

Elishakoff, I ;

Ramos, A. J. A. ;

Rosario Miranda, L. G. .

IMA JOURNAL OF APPLIED MATHEMATICS, 2019, 84 (04) :763-796

[3] Asymptotic behavior of weakly dissipative Bresse-Timoshenko system on influence of the second spectrum of frequency [J].

Almeida Junior, D. S. ;

Ramos, A. J. A. ;

Santos, M. L. ;

Gutemberg, L. R. M. .

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2018, 98 (08) :1320-1333

[4] On the nature of dissipative Timoshenko systems at light of the second spectrum of frequency [J].

Almeida Junior, D. S. ;

Ramos, A. J. A. .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2017, 68 (06)

[5] Exponential stability for a plate equation with p-Laplacian and memory terms [J].

Andrade, D. ;

Jorge Silva, M. A. ;

Ma, T. F. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2012, 35 (04) :417-426

[6]

[Anonymous], 1969, Quelques mthodes de rsolution des problmes aux limites non linaires

[7]

[Anonymous], 2019, MESA

[8]

[Anonymous], P IUTAM S PROB MECH

[9] An Exponential Stability Result of a Timoshenko System with Thermoelasticity with Second Sound and in the Presence of Delay [J].

Apalara, Tijani A. ;

Messaoudi, Salim A. .

APPLIED MATHEMATICS AND OPTIMIZATION, 2015, 71 (03) :449-472

[10] Existence and general stabilization of the Timoshenko system of thermo-viscoelasticity of type III with frictional damping and delay terms [J].

Chen, Miaomiao ;

Liu, Wenjun ;

Zhou, Weican .

ADVANCES IN NONLINEAR ANALYSIS, 2018, 7 (04) :547-569

← 1 2 3 →