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The Quarterly Journal of Mechanics and Applied Mathematics 1980 33(1):1-21; doi:10.1093/qjmam/33.1.1
© 1980 by Oxford University Press
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ON THE THEORY OF DIFFUSION IN MEDIA WITH DOUBLE DIFFUSIVITY I. BASIC MATHEMATICAL RESULTS

ELIAS C. AIFANTIS and JAMES M. HILL

( Department of Theoretical and Applied Mechanics, University of Illinois Urbana-Champaign, Urbana, Illinois 61801 )

The theory of diffusion in media with double diffusivity is described by a system of coupled linear partial differential equations of parabolic type. Uniqueness, maximum principles and basic source solutions are established in Part I of the paper. In Part II a technique for solving boundary-value problems is developed and applied to certain physically interesting cases. The results substantiate the theory and provided it with a definite form amenable to experimental verification.


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