Boundary Value Problems on Semi-Infinite Intervals.

Citation

Lentini Gil, Marianela (1978) Boundary Value Problems on Semi-Infinite Intervals. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/BZTP-PR15. https://resolver.caltech.edu/CaltechETD:etd-07072006-153103

Abstract

A theory of existence and uniqueness of bounded solutions of linear and nonlinear boundary value problems over a semi-infinite interval is developed. A numerical method for solving such problems is proposed. The method uses only finite intervals and convergence is proven as the length of the interval goes to infinity. This work is extended to problems over 0 <= t < [infinity] with a regular singular point at t = 0. The techniques developed are applied to solve three problems. i) The beam equation representing a semi-infinite pile imbedded in soil. Such problems are of interest in structural and foundation engineering. ii) An eigenvalue problem representing the solution of the Schrodinger equation for an ion of the hydrogen-molecule with fixed nuclei. iii) The Navier-Stokes equations for the von Karman swirling flow. For this problem the existence of multiple solutions has recently been discovered. We discover an additional branch of solutions and reproduce the previous results in a much simpler and more efficient manner. Our results clearly suggest that an infinite family of branches of solutions exist for this problem.

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