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IMA Journal of Applied Mathematics Advance Access published online on April 17, 2009
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxp018
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© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Global solution for a quasi-linear plate system with boundary memory damping

Qiong Zhang{dagger}

Department of Mathematics, Beijing Institute of Technology, Beijing 100081, People's Republic of China

{dagger} Email: zhangqiong{at}bit.edu.cn, qiongzhg{at}gmail.com

Received on August 28, 2007; Revision received February 12, 2009. In this work, we consider a quasi-linear plate model with boundary memory damping. We prove that this system has a unique global solution when the initial data are small enough and the non-linear coefficient function, the memory damping as well as the geometry of the domain satisfy suitable assumptions. We also prove the exponential decay of the energy of the system.

Keywords: global solution; quasi-linear system; boundary memory damping; exponential stability.


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