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ELASTIC MEMBRANE EQUATION WITH MEMORY TERM AND NONLINEAR BOUNDARY DAMPING:GLOBAL EXISTENCE,DECAY AND BLOWUP OF THE SOLUTION |
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| Authors: | Abderrahmane ZARA Nasser-eddine TATAR Salem ABDELMALEK |
| Institution: | 1. Depatment of Mathematics and Informatic, Cheikh El Arbi Tébessi University, 12002 Tébessa, Algeria 2. Depatment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals,Dhahran 31261,Saudi Arabia 3. Depatment of Mathematics, College of Sciences, Yanbu, Taibah University, Saudi Arabia; Depatment of Mathematics and Informatic, Cheikh El Arbi Tébessi University, 12002 Tébessa, Algeria |
| 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. |
| Keywords: | elastic membrane equation global existence boundary damping boundarysource general decay blowup |
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