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28th Southeastern-Atlantic Regional Conference on Differential Equations
October 10-11, 2008
University of Arkansas at Little Rock
Little Rock Arkansas, USA |
|
Organizers
Eric R. Kaufmann, Nickolai Kosmatov
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On the variational characterization of solutions to a nonsmooth Cahn-Hilliard equation
by
Stephen Robinson
Wake Forest University
Coauthors: Pavel Drabek, University of West Bohemia
Consider the functional
|
J(u)= |
e2
2
|
|
ó
õ
|
1
0
|
|u'|2dx+ |
ó
õ
|
1
0
|
F(u)dx, u ∈ W1, 2(0, 1), |
|
where F is a double-well potential such as F(u)=(1-u2)2.
This functional represents the total free energy in models of phase transition.
In this talk I describe how the complete list of critical points for J can be found and then classified as either minima or saddle points. Of particular interest will be some rather surprising continua of critical points that only appear when F loses its smoothness at u=±1.
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Date received: September 9, 2008
Copyright © 2008 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 # caww-25.