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
Copyright Date
1989
Language
en
Proquest ID
AAI8920177
File Format
application/pdf
File Size
124 pages
Recommended Citation
Park, Sang Ro, "The phenomenon of quenching in the presence of convection " (1989). Retrospective Theses and Dissertations. 9232.
https://lib.dr.iastate.edu/rtd/9232