Degree Type

Dissertation

Date of Award

2008

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Howard Levine

Second Advisor

Elgin Johnston

Third Advisor

Leslie Hogben

Abstract

The system ut = uxx - (uvx)x, vt = u - Av is considered where A is a non-negative, self-adjoint operator which commutes with the Laplacian. The operator is considered to have eigenvalues lambda n = nrholambda1, and the system is considered on [0,1] x [0,T] with homogeneous Neumann boundary conditions. The operators which lead to global solutions and those that lead to solutions which blow up in finite time are considered as a function of rho, using an application of the methods of Hillen and Potapov [Math. Methods Appl. Sci., 27 (2004), pp. 1783-1801] to analyze the global case and those of Halverson, Levine, and Renclawowicz [Siam J. Appl. Math., 65 (2004), pp. 336--360; 66 (2005), pp. 361--364] to analyze the finite time blowup case. Some numerical results are provided to back up the analysis. Some questions and directions for future study are posed.

DOI

https://doi.org/10.31274/rtd-180813-16867

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Matthew Alan Halverson

Language

en

Proquest ID

AAI3307081

OCLC Number

243695534

ISBN

9780549543312

File Format

application/pdf

File Size

68 pages

Included in

Mathematics Commons

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