# American Institute of Mathematical Sciences

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January  2002, 8(1): 219-236. doi: 10.3934/dcds.2002.8.219

## The existence of the heat flow of H-systems

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

Received  January 2001 Revised  August 2001 Published  October 2001

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.
Citation: Y. Chen, S. Levine. The existence of the heat flow of H-systems. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 219-236. doi: 10.3934/dcds.2002.8.219
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