Wiginton, C. Lamar2022-01-272022-01-27197213683504https://hdl.handle.net/10657/8630This 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.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Thesisreformatted digital