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Asymptotic Properties of a Nonlinear Diffusion Process Arising in Articular Cartilage

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Asymptotic Properties of a Nonlinear Diffusion Process Arising in Articular Cartilage

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Title: Asymptotic Properties of a Nonlinear Diffusion Process Arising in Articular Cartilage
Author: Mow, Van C.; Eisenfeld, Jerome
Abstract: There has been considerable effort put forth to analyse degenerative Joint diseases in terms of the principles of mechanics and hydrodynamics [8]. This effort has led to mathematical models which are systems of nonlinear partial differential equations (see e.g., [6] and [7]). The mathematical models are based on assumptions concerning the nature of the physical system which are not a priori known. Therefore laboratory experiments are performed with an eye towards validating the mathematical models. This paper deals with a particular mathematical model, a nonlinear diffusion equation, which has been proposed by Mow and Monsour [4], [5] to describe the stress relaxation of articular cartilage. More precisely, the stress relaxation function f(t) is related to a solution u(x,t) of a nonlinear PDE problem (see (1.1)-(1.4) below). In this paper we analytically determine the behavior of f(t) (Theorem 1). The consistency of these results to already existing theory and experimental findings is discussed in [1].
URI: http://hdl.handle.net/10106/2304
Date: 1977-01

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