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Fourth Mississippi State Conference on Differential Equations and Computational Simulations
May 21-22, 1999
Mississippi State University and Electronic Journal of Differential Equations
Starkville, MS, USA

Organizers
Ratnasingham Shivaji, Bharat Soni, Jianping Zhu (Program Chair)

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Diffusion in Nonhomogeneous Environment with Active Diffusion Interface Conditions
by
Scott Caldwell
Mississippi State University
Coauthors: J.B. Garner, R. Shivaji

Boundary value problems of the type
pi-1( x) { pi( x) gi(x, yi) yi¢} ¢=fi( x, yi);   i £ x £ i-1,   i=1, 2

y1¢( 0) = h1( y1( 0) )        y2( 2) = h2( y2¢( 2))


-ap1( 1) g1( 1, y1(1) ) y1¢( 1) = H( y1(1) , y2( 1) ) +h3( y1( 1)) -k1


-bp2( 1) g2( 1, y2( 1)) y2¢( 1) = H( y1( 1), y2( 1) ) -h4( y2( 1) )+k2

are used to model steady state diffusion of a specimen in a two patch nonhomogeneous environment.. It is assumed that the interaction between the two patches is by nonpassive diffusion. Existence and uniqueness results are obtained by matching solutions for each patch so that the interface conditions are satisfied.

Date received: April 9, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacr-62.