数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (1): 84-106.doi: 10.1016/S0252-9602(12)60196-9

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ELASTIC MEMBRANE EQUATION WITH MEMORY TERM AND NONLINEAR BOUNDARY DAMPING: GLOBAL EXISTENCE, DECAY AND BLOWUP OF THE SOLUTION

Abderrahmane ZARAÏ|Nasser-eddine TATAR|Salem ABDELMALEK   

  1. Depatment of Mathematics and Informatic, Cheikh El Arbi T´ebessi University, 12002 T´ebessa, Algeria; Depatment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia; Depatment of Mathematics, College of Sciences, Yanbu, Taibah University, Saudi Arabia;Depatment of Mathematics and Informatic, Cheikh El Arbi T´ebessi University, 12002 T´ebessa, Algeria
  • 收稿日期:2011-10-12 修回日期:2012-06-17 出版日期:2013-01-20 发布日期:2013-01-20

ELASTIC MEMBRANE EQUATION WITH MEMORY TERM AND NONLINEAR BOUNDARY DAMPING: GLOBAL EXISTENCE, DECAY AND BLOWUP OF THE SOLUTION

Abderrahmane ZARAÏ|Nasser-eddine TATAR|Salem ABDELMALEK   

  1. Depatment of Mathematics and Informatic, Cheikh El Arbi T´ebessi University, 12002 T´ebessa, Algeria; Depatment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia; Depatment of Mathematics, College of Sciences, Yanbu, Taibah University, Saudi Arabia;Depatment of Mathematics and Informatic, Cheikh El Arbi T´ebessi University, 12002 T´ebessa, Algeria
  • Received:2011-10-12 Revised:2012-06-17 Online:2013-01-20 Published:2013-01-20

摘要:

In this paper we consider the Elastic membrane equation with memory term and nonlinear boundary damping. Under some appropriate assumptions on the relaxation function h and with certain initial data, the global existence of solutions and a general decay for the energy are established using the multiplier technique. 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 nonlinear damping.

关键词: elastic membrane equation, global existence, boundary damping, boundary source, general decay, blowup

Abstract:

In this paper we consider the Elastic membrane equation with memory term and nonlinear boundary damping. Under some appropriate assumptions on the relaxation function h and with certain initial data, the global existence of solutions and a general decay for the energy are established using the multiplier technique. 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 nonlinear damping.

Key words: elastic membrane equation, global existence, boundary damping, boundary source, general decay, blowup

中图分类号: 

  • 35L05