A free boundary problem for an elastic material

Pages: 10 - 17, Issue Special, September 2007

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Toyohiko Aiki - Department of Mathematics, Faculty of Education, Gifu University, Yanagido 1-1, Gifu, Gifu, 501-1193, Japan, Japan (email)

Abstract: 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:  elastic material, free boundary problem, nonlinear strain
Mathematics Subject Classification:  Primary: 74B20, 35G25; Secondary: 74B99

Received: September 2006;      Revised: August 2007;      Published: September 2007.