Existence and exponential stability of solutions for a Balakrishnan-Taylor quasilinear wave equation with strong damping and localized nonlinear damping

被引：1

作者：

Hajjej, Zayd ^{[1
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2024年 / 31卷 / 04期

关键词：

Quasilinear wave equation; Balakrishnan-Taylor damping; strong damping; exponential stability; VISCOELASTIC EQUATION; GENERAL DECAY; VARIABLE-COEFFICIENTS; GLOBAL EXISTENCE; STABILIZATION;

D O I：

10.1515/gmj-2023-2105

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the paper, we study a Balakrishnan-Taylor quasilinear wave equation |z(t)|(alpha )z(tt )- Delta z(tt )- (xi(1 )+ xi(2)parallel to del(z)parallel to(2 )+ sigma(del z, del z(t)))Delta z - Delta z(t )+ beta(x)f(z(t)) + g(z) = 0 in a bounded domain of R-n with Dirichlet boundary conditions. By using Faedo-Galerkin method, we prove the existence of global weak solutions. By the help of the perturbed energy method, the exponential stability of solutions is also established.

引用

页码：615 / 626

页数：12

共 23 条

[1] EXISTENCE AND GENERAL DECAY OF BALAKRISHNAN-TAYLOR VISCOELASTIC EQUATION WITH NONLINEAR FRICTIONAL DAMPING AND LOGARITHMIC SOURCE TERM [J].

Al-gharabli, Mohammad ;

Balegh, Mohamed ;

Feng, Baowei ;

Hajjej, Zayd ;

Messaoudi, Salim A. .

EVOLUTION EQUATIONS AND CONTROL THEORY, 2021, :1149-1173

[2]

[Anonymous], 1998, Distrubutions Espace de Sobolev Application

[3]

Balakrishnan A. V., 1989, P DAMP 89 FLIGHT DYN, pFDC1

[4]

BASS RW, 1991, PROCEEDINGS OF THE 30TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-3, P1633, DOI 10.1109/CDC.1991.261683

[5] Existence and uniform decay for a non-linear viscoelastic equation with strong damping [J].

Cavalcanti, MM ;

Cavalcanti, VND ;

Ferreira, J .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2001, 24 (14) :1043-1053

[6]

Clark H. R., 2022, ELECTRON J QUAL THEO, V2002

[7]

Ferreira J., 1992, INT J MATH MATH SCI, V15, P543

[8]

Ferreira J., 1999, 9th Int. Coll. on Diff. Eqs., P155

[9] Long-Time Dynamics of Balakrishnan-Taylor Extensible Beams [J].

Gomes Tavares, E. H. ;

Jorge Silva, M. A. ;

Narciso, V. .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2020, 32 (03) :1157-1175

[10] Stabilization for the Wave Equation with Variable Coefficients and Balakrishnan-Taylor Damping [J].

Ha, Tae Gab .

TAIWANESE JOURNAL OF MATHEMATICS, 2017, 21 (04) :807-817

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