Exponential stability and blow up for a problem with Balakrishnan–Taylor damping

Demonstratio mathematica

article

Nasser-eddine Tatar¹  Abderrahmane Zaraï² 

[1] King Fahd University of Petroleum and Minerals;Cheikh El Arbi Tébessi University

关键词: Balakrishnan–Taylor damping;    exponential stability;    memory term;    relaxation function;    viscoelasticity;   

DOI  :  10.1515/dema-2013-0297

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

This work is devoted to the study of a nonlinear viscoelastic Kirchhoff equation with Balakrishnan–Taylor damping. We show that the weak dissipation produced by the memory term is strong enough to stabilize solutions exponentially. Also, we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a stronger damping.

【 授权许可】

CC BY