This work was suggested by a paper by V. W. Bolie in which he develops a non-linear impedance theory for bioelectrodes. In his work, he arrives at a pair of diffusion equations with the interesting feature that one of the boundary conditions is expressed as a definite integral. Since we are unaware of any work in which a parabolic equation is subjected to this type of boundary condition, we naturally asked the question as to whether such a problem has a solution; and if it does, is the solution unique? In this paper we answer these questions for the linear diffusion problem.
Proceedings of the Iowa Academy of Science
©1963 Iowa Academy of Science, Inc.
Deckert, K. L. and Maple, C. G.
"Solutions for Diffusion Equations With Integral Type Boundary Conditions,"
Proceedings of the Iowa Academy of Science, 70(1), 354-361.
Available at: https://scholarworks.uni.edu/pias/vol70/iss1/60