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Southeastern-Atlantic Regional Conference on Differential Equations
October 19-20, 2007
Murray State University
Murray, Kentucky, USA |
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Organizers
K. Renee Fister, Maeve McCarthy
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Blow-up of the Solution for Nonlinear Parabolic Problems
by
W. Y. Chan
Department of Mathematics, Southeast Missouri State University
In this talk, we discuss the existence and
uniqueness of the classical solution of the following nonlinear parabolic
problem,
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xqut=( um) xx+bf( u) in (0, 1) ×( 0, T) , |
|
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u( x, 0) = u0( x) in [ 0, 1] , u( 0, t) = 0=u( 1, t) for t ∈ ( 0, T), |
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where m > 1, b is a positive number, q is a nonnegative number, u0( x) is a positive function, and f( u) is a
given function. Furthermore, a criterion for u to blow up in a finite time
is given.
Date received: September 3, 2007
Copyright © 2007 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # cavc-16.