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

doi:10.1016/S0252-9602(12)60196-9

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

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

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

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/Abstract

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:

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

中图分类号:

35L05

Abderrahmane ZARAI, Nasser-eddine TATAR, Salem ABDELMALEK. ELASTIC MEMBRANE EQUATION WITH MEMORY TERM AND NONLINEAR BOUNDARY DAMPING: GLOBAL EXISTENCE, DECAY AND BLOWUP OF THE SOLUTION[J]. 数学物理学报(英文版), 2013, 33(1): 84-106.

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

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

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