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Problems in nonlinear diffusion

Citation

Witelski, Thomas P. (1995) Problems in nonlinear diffusion. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-10252007-112314

Abstract

A variety of effects can occur from different forms of nonlinear diffusion or from coupling of diffusion to other physical processes. I consider two such classes of problems; first, the analysis of behavior of diffusive solutions of the generalized porous media equation, and second, the study of stress-driven diffusion in solids. The porous media equation is a nonlinear diffusion equation that has applications to numerous physical problems. By combining classical techniques for the study of similarity solutions with perturbation methods, I have examined some new initial-boundary value problems for the porous media equation, including "stopping" and "merging" problems. Using matched asymptotic expansions and boundary layer analysis, I have shown that the initial deviations from similarity solution form in these problems are asymptotic beyond all orders. Applications of these studies to the Cahn-Hilliard and Fisher's equations are also considered. In my examination of stress-driven diffusion, I consider models for the behavior of systems in the emerging technological field of viscoelastic diffusion in polymer materials. Using asymptotic analysis, I studied some of the non-traditional effects, shock formation in particular, that occur in initial-boundary value problems for these models. Phase-interface traveling waves for "Case II" diffusive transport were also studied, using phase plane techniques.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Thesis Availability:Restricted to Caltech community only
Research Advisor(s):
  • Cohen, Donald S.
Thesis Committee:
  • Unknown, Unknown
Defense Date:21 April 1995
Record Number:CaltechETD:etd-10252007-112314
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-10252007-112314
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4259
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:25 Oct 2007
Last Modified:26 Dec 2012 03:06

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