On an equation modeling the flow in the canal of Schlemm.
In a recent paper Tandon and Autar showed how the model equations for flow of aqueous humor in the canal of Schlemm with a flexible inner wall can be reduced to a second-order boundary value problem for the fluid pressure. They then proceeded to solve this using an approximate iterative scheme. In this paper we show how the problem can be reduced to a first-order one for the canal thickness that can be analyzed in the phase plane. This crucial reduction and subsequent analysis reveals important properties of the solution not apparent from the approximate treatment of Tandon and Autar. Furthermore, by solving the first-order problem exactly in terms of definite integrals, the important questions of existence and uniqueness for given parameter values can be addressed.
Grundy
R E
RE
Department of Mathematical Sciences, University of St. Andrews, North Haugh, Fife, Scotland.
D001082:Aqueous Humor / Q000502:physiology; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D012590:Sclera / Q000502:physiology*