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

Abstract

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

CLC Number:

35L05

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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.

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