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The Quarterly Journal of Mechanics and Applied Mathematics 1980 33(1):23-42; doi:10.1093/qjmam/33.1.23
© 1980 by Oxford University Press
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ON THE THEORY OF DIFFUSION IN MEDIA WITH DOUBLE DIFFUSIVITY II. BOUNDARY-VALUE PROBLEMS

JAMES M. HILL and ELIAS C. AIFANTIS

( Department of Theoretical and Applied Mechanics, University of Illinois at 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. Qualitative aspects and basic source solutions were considered in Part I of this paper. In Part II, typical initial boundary-value problems are formulated and solved. The solution technique is based on establishing a correspondence between solutions of the present theory and the ‘classical’ diffusion theory. This process avoids inverting complicated Laplace transforms and implies that solutions to the present initial boundary-value problems can be expressed in terms of ‘classical’ diffusion functions.


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