Existence and energy decay of solution to a nonlinear viscoelastic two-dimensional beam with a delay

被引：6

作者：

Lekdim, Billal ^{[1
,2
]}

Khemmoudj, Ammar ^{[2
]}

机构：

[1] Univ Ziane Achour Djelfa, Dept Math, Djelfa 17000, Algeria

[2] Univ Sci & Technol Houari Boumediene, Fac Math, Lab SDG, POB 32, Algiers 16111, Algeria

来源：

MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING | 2021年 / 32卷 / 03期

关键词：

Viscoelastic damping; Distributed delay term; Nonlinear tension; Exponential decay; Lyapunov method;

D O I：

10.1007/s11045-021-00766-z

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A longitudinal and transversal vibrations of the beam with nonlinear tension, a viscoelastic damping and distributed delay term is studied. Using the Faedo-Galerkin method, the well-posedness of the problem is established. A uniform decay result is proved by multiplier method.

引用

页码：915 / 931

页数：17

共 35 条

[1]

Aili M., 2019, REND CIRC MAT PALERM, V2, P1

[2] Decay estimates for second order evolution equations with memory [J].

Alabau-Boussouira, Fatiha ;

Cannarsa, Piermarco ;

Sforza, Daniela .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (05) :1342-1372

[3]

Apalara TA, 2014, ELECTRON J DIFFER EQ

[4]

AUBIN JP, 1963, CR HEBD ACAD SCI, V256, P5042

[5]

Benaissa A, 2014, INT J DYN SYST DIFFE, V5, P1

[6]

Bland D. R., 2016, The Theory of Linear Viscoelasticity

[7] FOUNDATIONS OF LINEAR VISCOELASTICITY [J].

COLEMAN, BD ;

NOLL, W .

REVIEWS OF MODERN PHYSICS, 1961, 33 (02) :239-249

[8] Global existence and exponential decay of the solution for a viscoelastic wave equation with a delay [J].

Dai, Qiuyi ;

Yang, Zhifeng .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2014, 65 (05) :885-903

[9] Boundary control of transverse motion of marine risers with actuator dynamics [J].

Do, K. D. ;

Pan, J. .

JOURNAL OF SOUND AND VIBRATION, 2008, 318 (4-5) :768-791

[10]

Feng, 2016, Z ANGEW MATH PHYS, V1, P1

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