Asymptotic properties of a nonlinear diffusion process arising in articular cartilage

摘要

Stress relaxation experiments in articular cartilage studies give rise to a nonlinear diffusion process. The paper demonstrates that the nonlinear model admits a solution which possesses certain salient features that are observed experimentally. A relaxation constant is defined for the nonlinear model in order to examine the asymptotic behavior of solutions as time approaches infinity. An explicit formula relating the relaxation constant to the nonlinear permeability function, and the displacement at the “motor cutoff time” is derived. Finally, upper and lower bounds to the solution and certain of its derivatives are provided.