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2002, Volume 8, Issue 1: 219-236. Doi: 10.3934/dcds.2002.8.219

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The existence of the heat flow of H-systems

Y. Chen^1, and
S. Levine^2,

1.
P.O. Box 118105, Department of Mathematics, University of Florida, Gainesville, Florida 32611
2.
440 College Hall, Department of Mathematics and Computer Science, Duquesne University, Pittsburgh, Pennsylvania 15282

Received: January 2001

Revised: August 2001

Published: January 2002

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Abstract

In this paper, we show the existence of a unique, regular solution to the flow of the H-system with Dirichlet boundary condition. The solution exists at least up until the time of energy concentration. If this solution satisfies a certain energy inequality, then it can be continued to a global solution with the exception of at most finitely many singularities. The behavior of the singularities also are discussed.

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Mathematics Subject Classification: Primary: 54C40, 14E20; Secondary: 46E25, 20C20.

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