Lentini Gil, Marianela (1978) Boundary value problems over semi-infinite intervals. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-07072006-153103
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.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Engineering and Applied Science|
|Major Option:||Applied And Computational Mathematics|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||2 May 1978|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||31 Jul 2006|
|Last Modified:||26 Dec 2012 02:54|
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