Attractors for a class of wave equations with nonlocal structural energy damping

被引：1

作者：

Bezerra, Flank D. M. ^{[1
]}

Liu, Linfang ^{[2
]}

Narciso, Vando ^{[3
]}

机构：

[1] Univ Fed Paraiba, Dept Math, Univ City-Campus 1, BR-58051900 Joao Pessoa, PB, Brazil

[2] Northwest Univ, Sch Math, Xian 710119, Shaanxi, Peoples R China

[3] Univ Estado Mato Grosso, Ctr Exact & Earth Sci, BR-79804970 Dourados, MS, Brazil

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2024年 / 31卷 / 06期

关键词：

Energy damping; Global attractor; Wave equation; Well-posedness; DEGENERATE; BEHAVIOR;

D O I：

10.1007/s00030-024-01000-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the well-posedness and long-time dynamics for a class of wave equations with a nonlocal structural energy damping. The main result establishes that for each exponent beta is an element of (0,1/2 + & varepsilon;) of the structural term, for a small & varepsilon; > 0, the corresponding problem has a compact global attractor U-beta, which coincides with the unstable manifold M-beta(N) emanating from the set N of stationary points. This class of problems whose dissipation intensity depends on the energy of the system has connection with flight structure models, see NASA-AirForce reports (Balakrishnan in A theory of nonlinear damping in flexible structures. Stabilization of flexible structures, 1988; Balakrishnan and Taylor in Proceedings Damping 89, Flight Dynamics Lab and Air Force Wright Aeronautical Labs, WPAFB, 1989).

引用

页数：24

共 25 条

[1] Compactness of trajectories to some nonlinear second order evolution equations and applications [J].

Aloui, Faouzia ;

Ben Hassen, Imen ;

Haraux, Alain .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2013, 100 (03) :295-326

[2]

Amann H., 1995, ABSTRACT LINEAR THEO, V1, DOI DOI 10.1007/978-3-0348-9221-6

[3]

[Anonymous], 1988, Asymptotic behavior of dissipative systems. Mathematical surveys and monographs

[4] Quasi-stability and upper semicontinuity for coupled parabolic equations with memory [J].

Aouadi, Moncef .

STUDIES IN APPLIED MATHEMATICS, 2020, 145 (03) :586-621

[5] Global and exponential attractors for extensible thermoelastic plate with time-varying delay [J].

Aouadi, Moncef .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (05) :4079-4115

[6]

Babin A., 1992, STUDIES MATH ITS APP, V25

[7]

Babin A. V., 1997, J. Math. Sci., V87, P3304

[8]

Balakrishnan A.V., 1989, P DAMP 89 FLIGHT DYN

[9]

Balakrishnan A. V., 1988, Stabilization of Flexible Structures, P1

[10] Dynamics for a class of energy beam models with non-constant material density [J].

Bezerra, Flank D. M. ;

Liu, Linfang ;

Narciso, Vando .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2024, 75 (01)

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