Acta mathematica scientia, Series B >
ELASTIC MEMBRANE EQUATION WITH MEMORY TERM AND NONLINEAR BOUNDARY DAMPING: GLOBAL EXISTENCE, DECAY AND BLOWUP OF THE SOLUTION
Received date: 2011-10-12
Revised date: 2012-06-17
Online published: 2013-01-20
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.
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]. Acta mathematica scientia, Series B, 2013 , 33(1) : 84 -106 . DOI: 10.1016/S0252-9602(12)60196-9
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