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IMA Journal of Applied Mathematics Advance Access originally published online on July 27, 2008
IMA Journal of Applied Mathematics 2009 74(1):97-106; doi:10.1093/imamat/hxn020
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A higher-order Boussinesq equation in locally non-linear theory of one-dimensional non-local elasticity

N. Duruk and A. Erkip

Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla 34956, Istanbul, Turkey

H. A. Erbay{dagger}

Department of Mathematics, Isik University, Sile 34980, Istanbul, Turkey

{dagger} Email: erbay{at}isikun.edu.tr

Received on November 26, 2007; Revision received May 23, 2008. Accepted on June 10, 2008

In one space dimension, a non-local elastic model is based on a single integral law, giving the stress when the strain is known at all spatial points. In this study, we first derive a higher-order Boussinesq equation using locally non-linear theory of 1D non-local elasticity and then we are able to show that under certain conditions the Cauchy problem is globally well-posed.

Keywords: higher-order Boussinesq equation; non-local elasticity; global well-posedness; Cauchy problem.


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