BLOW-UP OF SOLUTION FOR A VISCOELASTIC WAVE EQUATION WITH DELAY

被引：10

作者：

Wu, Shun-Tang ^{[1
]}

机构：

[1] Natl Taipei Univ Technol, Gen Educ Ctr, Taipei 106, Taiwan

来源：

ACTA MATHEMATICA SCIENTIA | 2019年 / 39卷 / 01期

关键词：

blow up; nonlinear source; wave equation; delay; viscoelastic; TIME-VARYING DELAY; DYNAMIC BOUNDARY; GENERAL DECAY; STABILIZATION; STABILITY; RESPECT; SYSTEMS; TERM;

D O I：

10.1007/s10473-019-0124-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the following viscoelastic wave equation with delay vertical bar ut vertical bar(rho) u(tt) - Delta u - Delta u(tt) + integral(t)(0) g(t - s)Delta u(s)ds + mu(1)u(t)(x, t) + mu(2)u(t)(x,t - tau ) = b vertical bar u vertical bar(p-2) u in a bounded domain. Under appropriate conditions on mu(1), mu(2), the kernel function g, the nonlinear source and the initial data, there are solutions that blow up in finite time.

引用

页码：329 / 338

页数：10

共 26 条

[1] 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

[2] Two examples of ill-posedness with respect to time delays revisited [J].

Datko, R .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1997, 42 (04) :511-515

[3] 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

[4] AN EXAMPLE ON THE EFFECT OF TIME DELAYS IN BOUNDARY FEEDBACK STABILIZATION OF WAVE-EQUATIONS [J].

DATKO, R ;

LAGNESE, J ;

POLIS, MP .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1986, 24 (01) :152-156

[5] Asymptotic behavior for a weak viscoelastic wave equations with a dynamic boundary and time varying delay term [J].

Ferhat M. ;

Hakem A. .

Journal of Applied Mathematics and Computing, 2016, 51 (1-2) :509-526

[6] A blow-up result in a nonlinear abstract evolution system with delay [J].

Kafini, Mohammad ;

Messaoudi, Salim A. ;

Nicaise, Serge .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2016, 23 (02)

[7] A Blow-Up Result in a Nonlinear Wave Equation with Delay [J].

Kafini, Mohammad ;

Messaoudi, Salim A. .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2016, 13 (01) :237-247

[8] Existence and asymptotic stability of a viscoelastic wave equation with a delay [J].

Kirane, Mokhtar ;

Said-Houari, Belkacem .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2011, 62 (06) :1065-1082

[9] Energy decay for a nonlinear wave equation of variable coefficients with acoustic boundary conditions and a time-varying delay in the boundary feedback [J].

Li, Jing ;

Chai, Shugen .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 112 :105-117

[10] Asymptotic stability for a non-autonomous full von Karman beam with thermo-viscoelastic damping [J].

Liu, Wenjun ;

Chen, Kewang ;

Yu, Jun .

APPLICABLE ANALYSIS, 2018, 97 (03) :400-414

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