Degree Type

Dissertation

Date of Award

1989

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Howard A. Levine

Abstract

In this paper, we present several results concerning the long time behavior of positive solutions of Burgers' equation u[subscript] t = u[subscript]xx+[epsilon] uu[subscript]x,[epsilon]>0,00,u(x,0) given, subject to one of four pairs of boundary conditions:(UNFORMATTED TABLE OR EQUATION FOLLOWS) (A[subscript]1) u(0,t) = 0,u[subscript] x(1,t) = a(1 - u(1,t))[superscript]-p, t > 0, &(B[subscript]1) u(1,t) = 0,u[subscript]x(0,t) = -a(1 - u(0,t))[superscript]-p, t > 0, &(C[subscript]1) u(0,t) = 0,u[subscript]x(1,t) = a[over] u[superscript]p(1,t), t > 0, & or &(D[subscript]1) u[subscript]x(0,t) = -a[over] u[superscript]p(1,t), u(1,t) = 0, t > 0, & where 0 0. (TABLE/EQUATION ENDS);A complete stability-instability analysis is given. It is shown that for (A) and (B) some solutions quench (reach one in finite time) and that when this happens u[subscript] t(1,t) blows up at the same time. Generalizations replacing uu[subscript] x by (f(u))[subscript]x and (1 - u)[superscript]-p or a[over] u[superscript] p(1,t) by g(u) are discussed with special emphasis on the case g(u) = au[superscript] p - [epsilon][over] 2 u[superscript]2.

DOI

https://doi.org/10.31274/rtd-180813-11523

Publisher

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

Copyright Owner

Sang Ro Park

Language

en

Proquest ID

AAI8920177

File Format

application/pdf

File Size

124 pages

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Included in

Mathematics Commons

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