Asymptotic Properties of a Nonlinear Diffusion Process Arising in Articular Cartilage
Mow, Van C.
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There has been considerable effort put forth to analyse degenerative Joint diseases in terms of the principles of mechanics and hydrodynamics . This effort has led to mathematical models which are systems of nonlinear partial differential equations (see e.g.,  and ). 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 ,  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 .