Asymptotic Behavior for a Viscoelastic Kirchhoff-Type Equation with Delay and Source Terms

被引：4

作者：

Boumaza, Nouri ^{[1
,2
]}

Saker, Meriem ^{[1
,2
]}

Gheraibia, Billel ^{[2
,3
]}

机构：

[1] Larbi Tebessi Univ, Dept Math & Comp Sci, Tebessa, Algeria

[2] Larbi Tebessi Univ, Lab Math Informat & Syst LAMIS, Tebessa, Algeria

[3] Larbi Ben MHidi Univ, Dept Math & Comp Sci, Oum El Bouaghi, Algeria

来源：

ACTA APPLICANDAE MATHEMATICAE | 2021年 / 171卷 / 01期

关键词：

Viscoelastic wave equation; Kirchhoff-type equation; Delay term; Global existence; General decay; Blow-up; 35B40; 35B44; 35L05; 35L75;

D O I：

10.1007/s10440-021-00387-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we consider a nonlinear viscoelastic Kirchhoff-type equation with delay and source terms in a bounded domain. Under an hypothesis between the weight of the delay term in the feedback and the weight of the weak damping term, we obtain a global existence of solutions and established the general decay rate, also we prove the finite time blow-up result of solutions with negative initial energy.

引用

页数：18

共 39 条

[1]

Adams R., 2003, SOBOLEV SPACES

[2] New general decay results in an infinite memory viscoelastic problem with nonlinear damping [J].

Al-Mandi, Adel M. ;

Al-Gharabli, Mohammad M. .

BOUNDARY VALUE PROBLEMS, 2019, 2019 (01)

[3]

[Anonymous], 1995, Differ. Integral Equ

[4] General decay and blowup of solutions for a degenerate viscoelastic equation of Kirchhoff type with source term [J].

Boumaza, Nouri ;

Gheraibia, Billel .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 489 (02)

[5] Exponential stability for the wave model with localized memory in a past history framework [J].

Cavalcanti, M. M. ;

Domingos Cavalcanti, V. N. ;

Jorge Silva, M. A. ;

de Souza Franco, A. Y. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (11) :6535-6584

[6] Frictional versus viscoelastic damping in a semilinear wave equation [J].

Cavalcanti, MM ;

Oquendo, HP .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2003, 42 (04) :1310-1324

[7] 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

[8] NOT ALL FEEDBACK STABILIZED HYPERBOLIC SYSTEMS ARE ROBUST WITH RESPECT TO SMALL TIME DELAYS IN THEIR FEEDBACKS [J].

DATKO, R .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1988, 26 (03) :697-713

[9] A general stability result for the semilinear viscoelastic wave model under localized effects [J].

Faria, J. C. O. ;

Jorge Silva, M. A. ;

Souza Franco, A. Y. .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2020, 56

[10] A general decay result for a viscoelastic equation in the presence of past and finite history memories [J].

Guesmia, Aissa ;

Messaoudi, Salim A. .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (01) :476-485

← 1 2 3 4 →