Analysis of a boundary value problem associated with laminar fluid flow

This dissertation considers the linear operator eigenvalue problem L(u) + su - a(u) = 0 subject to the boundary condition u = c for some real valued scalar c . It is shown that under certain conditions the problem is equivalent to solving the equation L(v) + sv = 0 subject to the boundary condition v = 0 . The analysis is applied to a linearized mathematical model for solving velocity profiles for laminar fluid flow in the entrance region of ducts. Existence and uniqueness of a solution are guaranteed for a large class of initial profiles. Numerical results are presented for a rectangular duct with 2 to 1 aspect ratio.