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Fourth Mississippi State Conference on Differential Equations and Computational Simulations
May 21-22, 1999
Mississippi State University and Electronic Journal of Differential Equations
Starkville, MS, USA |
|
Organizers
Ratnasingham Shivaji, Bharat Soni, Jianping Zhu (Program Chair)
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The Existence of Solutions to the Heat Flow of H-systems
by
Stacey Chastain
University of Florida
Coauthors: Yunmei Chen (University of Florida)
In this paper, we show the existence of a unique, regular solution to
the flow of the H-system,
|
ut-\triangle u=2H(u)ux /\ uy |
|
with
Dirichlet boundary condition, where H:R3 --> R is a Lipshitz
continuous function. The solution exists at least up until the time
of an energy concentration. If the solution satisfies a certain energy
inequality, then it can be extended to a global weak solution which is
regular with the exception of finitely many singularities. The
behavior of the solution at these singularities will also be discussed.
Date received: March 30, 1999
Copyright © 1999 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 # cacr-39.