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2007, 2007(Special): 10-17. doi: 10.3934/proc.2007.2007.10

A free boundary problem for an elastic material

Toyohiko Aiki 1,

1. 

Department of Mathematics, Faculty of Education, Gifu University, Yanagido 1-1, Gifu, Gifu, 501-1193, Japan

Received  September 2006 Revised  August 2007 Published  September 2007

In this paper we investigate the dynamics of an elastic material, for example, a spring with some weight. Such dynamics is usually represented by the ordinary differential equation for the length of the spring or the partial differential equation with the linear strain on a fixed domain. The main purpose of this paper is to propose a new free boundary problem with a nonlinear strain as a mathematical model for an elastic material. Also, we establish the wellposedness for initial boundary value problem with the nonlinear strain on the cylindrical domain.
Keywords: free boundary problem, nonlinear strain, elastic material.
Mathematics Subject Classification: Primary: 74B20, 35G25; Secondary: 74B99.
Citation: Toyohiko Aiki. A free boundary problem for an elastic material. Conference Publications, 2007, 2007 (Special) : 10-17. doi: 10.3934/proc.2007.2007.10
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