Comparison of One- and Three-Dimensional Models for Tracer Evolution in Tissue Cylinders
Leonard Sarason · SIAM Journal on Applied Mathematics · 1989
Eigenvalues of the time-reduced operator for a one-dimensional model for diffusion and transport of tracers in tissue cylinders are shown to be limits of some of the eigenvalues of the corresponding three-dimensional operator under an appropriate limiting process. The proof depends on the constructionof approximate eigenfunctions for the three-dimensional operators from eigenfunctions of the one-dimensional operator. Solutions of time-dependent problems with inhomogeneous boundary data are shownto converge to solutions of a one-dimensional time-dependent problem.