A nonlinear diffusion equation arising in the study of soft tissue

Author:
Mark H. Holmes

Journal:
Quart. Appl. Math. **41** (1983), 209-220

MSC:
Primary 73P05; Secondary 76Z05, 92A09

DOI:
https://doi.org/10.1090/qam/719505

MathSciNet review:
719505

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Abstract: A nonlinear diffusion equation which describes the deformation of a soft fluid-filled tissue is studied. The nonlinearity in the problem arises from the permeability of the elastic phase which for a number of tissues, such as articular cartilage, is strongly dependent on the strain. Moreover, for most tissues the exact dependence is not known, and so the functional dependence of the permeability on the strain is not determined until after the problem is solved. The approach uses perturbation methods for the diffusive boundary layers that occur in the problem and similarity solutions to solve the reduced problems. Once the solution is obtained, the permeability function is determined and some of the limitations of the present model of soft tissue are discussed.

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DOI:
https://doi.org/10.1090/qam/719505

Article copyright:
© Copyright 1983
American Mathematical Society