A blow-up result in a nonlinear abstract evolution system with delay

被引：24

作者：

Kafini, Mohammad ^{[1
]}

Messaoudi, Salim A. ^{[1
]}

Nicaise, Serge ^{[2
]}

机构：

[1] KFUPM, Dept Math & Stat, Dhahran 31261, Saudi Arabia

[2] Univ Valenciennes & Hainaut Cambresis, LAMAV, FR CNRS 2956, F-59313 Valenciennes 9, France

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2016年 / 23卷 / 02期

关键词：

Abstract evolution system; Delay; Second order; Blow up; GLOBAL NONEXISTENCE THEOREMS; WAVE-EQUATION; SOURCE TERMS; CAUCHY-PROBLEM; EXISTENCE; BOUNDARY; STABILIZATION; INSTABILITY; DISSIPATION; STABILITY;

D O I：

10.1007/s00030-016-0371-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider a second-order abstract evolution system with delay. We show that, under suitable conditions on the initial data and the involved functionals, the energy of solutions blows up in finite-time. We also give some concrete examples to illustrate our main result.

引用

页数：14

共 27 条

[1] Global Nonexistence for Nonlinear Kirchhoff Systems [J].

Autuori, Giuseppina ;

Pucci, Patrizia ;

Salvatori, Maria Cesarina .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 196 (02) :489-516

[2] REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NON-LINEAR EVOLUTION EQUATIONS [J].

BALL, JM .

QUARTERLY JOURNAL OF MATHEMATICS, 1977, 28 (112) :473-486

[3] Feedback stabilization of a class of evolution equations with delay [J].

Benhassi, E. M. Ait ;

Ammari, K. ;

Boulite, S. ;

Maniar, L. .

JOURNAL OF EVOLUTION EQUATIONS, 2009, 9 (01) :103-121

[4] EXISTENCE OF A SOLUTION OF THE WAVE-EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS [J].

GEORGIEV, V ;

TODOROVA, G .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 109 (02) :295-308

[5] INSTABILITY AND NONEXISTENCE OF GLOBAL SOLUTIONS TO NONLINEAR-WAVE EQUATIONS OF FORM PUTT = -AU + F(U) [J].

LEVINE, HA .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 192 :1-21

[6] SOME ADDITIONAL REMARKS ON NONEXISTENCE OF GLOBAL SOLUTIONS TO NONLINEAR-WAVE EQUATIONS [J].

LEVINE, HA .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1974, 5 (01) :138-146

[7] Global nonexistence theorems for quasilinear evolution equations with dissipation [J].

Levine, HA ;

Serrin, J .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1997, 137 (04) :341-361

[8] Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave equation [J].

Levine, HA ;

Park, SR ;

Serrin, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 228 (01) :181-205

[9] Locally distributed control and damping for the conservative systems [J].

Liu, KS .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1997, 35 (05) :1574-1590

[10]

Messaoudi S. A., 2003, COMMUN PUR APPL ANAL, V7, P379

← 1 2 3 →