BLOW-UP OF SOLUTIONS TO A VISCOELASTIC WAVE EQUATION WITH NONLOCAL DAMPING

被引：0

作者：

Li, Donghao ^{[1
]}

Zhang, Hongwei ^{[1
]}

Liu, Shuo ^{[1
]}

Hu, Qingiyng ^{[1
]}

机构：

[1] Henan Univ Technol, Dept Math, Zhengzhou 450001, Peoples R China

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2022年 / 11卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Viscoelastic wave equation; initial boundary value problem; nonlocal damping; blow-up; LONG-TIME DYNAMICS; GLOBAL NONEXISTENCE; EXPONENTIAL STABILITY; EVOLUTION-EQUATIONS; PLATE EQUATION; ATTRACTORS; EXISTENCE; MODEL; THEOREMS; INFINITY;

D O I：

10.3934/eect.2022009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The viscoelastic wave equation with nonlinear nonlocal weak damping is considered. The local existence of solutions is established. Under arbitrary positive initial energy, a finite-time blow-up result is proved by a new modified concavity method.

引用

页码：2017 / 2031

页数：15

共 37 条

[1] Stability results of coupled wave models with locally memory in a past history framework via nonsmooth coefficients on the interface
Akil, Mohammad
Badawi, Haidar
Nicaise, Serge
Wehbe, Ali
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (08) : 6950 - 6981
[2] Alshin A. B., 2011, GRUYTER SER NONLINEA, V15
[3] [Anonymous], 1997, DIFFER INTEGRAL EQU
[4] Blow up at infinity of solutions of polyharmonic Kirchhoff systems
Autuori, G.
Colasuonno, F.
Pucci, P.
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2012, 57 (2-4) : 379 - 395
[5] Global Nonexistence for Nonlinear Kirchhoff Systems
Autuori, Giuseppina
Pucci, Patrizia
Salvatori, Maria Cesarina
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 196 (02) : 489 - 516
[6] On nonlinear wave equations with degenerate damping and source terms
Barbu, V
Lasiecka, I
Rammaha, MA
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 357 (07) : 2571 - 2611
[7] Blow-up of generalized solutions to wave equations with nonlinear degenerate damping and source terms
Barbu, Viorel
Lasiecka, Irena
Rammaha, Mohammad A.
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2007, 56 (03) : 995 - 1021
[8] Cavalcanti MM, 2004, DIFFER INTEGRAL EQU, V17, P495
[9] Stability for extensible beams with a single degenerate nonlocal damping of Balakrishnan-Taylor type
Cavalcanti, M. M.
Cavalcanti, V. N. Domingos
Silva, M. A. Jorge
Narciso, V
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 290 : 197 - 222
[10] Exponential stability for the wave model with localized memory in a past history framework
Cavalcanti, M. M.
Domingos Cavalcanti, V. N.
Jorge Silva, M. A.
de Souza Franco, A. Y.
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (11) : 6535 - 6584

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