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

被引：0
作者：
Mohammad Kafini
Salim A. Messaoudi
Serge Nicaise
机构：
[1] KFUPM,Department of Mathematics and Statistics
[2] Université de Valenciennes et du Hainaut Cambrésis,undefined
来源：
Nonlinear Differential Equations and Applications NoDEA | 2016年 / 23卷
关键词：
Abstract evolution system; Delay; Second order; Blow up; 35B37; 35L55; 74D05; 93D15; 93D20;
D O I：
暂无
中图分类号：
学科分类号：
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
收藏
相关论文
共 44 条
  • [1] Ait Benhassi E.M.(2009)Feedback stabilization of a class of evolution equations with delay J. Evol. Equ. 9 103-121
  • [2] Ammari K.(2010)Global nonexistence for nonlinear Kirchhoff systems Arch. Rat. Mech. Anal. 196 489-516
  • [3] Boulite S.(1977)Remarks on blow up and nonexistence theorems for nonlinear evolutions equations Q. J. Math. Oxf. 28 473-486
  • [4] Maniar L.(1994)Existence of solutions of the wave equation with nonlinear damping and source terms J. Differ. Equ. 109 295-308
  • [5] Autuori G.(1997)A global nonexistence theorem for quasilinear evolution equation with dissipation Arch. Rat. Mech. Anal. 137 341-361
  • [6] Pucci P.(1974)Instability and nonexistence of global solutions of nonlinear wave equation of the form Trans. Am. Math. Soc. 192 1-21
  • [7] Salvatori M.C.(1974)Some additional remarks on the nonexistence of global solutions to nonlinear wave equation SIAM J. Math. Anal. 5 138-146
  • [8] Ball J.(1998)Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave equation J. Math. Anal. Appl. 228 181-205
  • [9] Georgiev V.(1997)Locally distributed control and damping for the conservative systems SIAM J. Control Optim. 35 1574-1590
  • [10] Todorova G.(2003)Blow up and global existence in a nonlinear viscoelastic wave equation Math. Nachr. 260 58-66
12345