The Existence of the Heat Flow of H-systems

  title={The Existence of the Heat Flow of H-systems},
  author={Yuehui Chen and Stephen Levine and Lawrence C. Evans},
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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Publications referenced by this paper.
Showing 1-10 of 10 references

The existence of surfaces of constant mean curvature with free boundaries

  • M Struwe
  • Math. Helv. no
  • 1988
Highly Influential
7 Excerpts

Heat flow for the equation of surfaces with prescribed mean curvature

  • Rey, Olivier
  • Math. Ann
  • 1991
Highly Influential
3 Excerpts

Linear and Quasi-linear Equations of Parabolic Type

  • O. A. Ladyzenskaja, V. A. Solonnikov, N. N. Ural’ceva
  • Trans. Math. Monographs
  • 1968
Highly Influential
5 Excerpts

Smooth Solutions of the Generalized System of Ferromagnetic Chain

  • Boling Guo, Haiyang Huang
  • Discrete Contin. Dynam. Systems
  • 2000

Geometric Evolution Problems of Nonlinear Partial Differential Equations in Differential Geometry

  • M Struwe
  • IAS Park City Math. Ser.,
  • 1992

Variational Methods

  • M. Struwe
  • Received January 2001; revised August
  • 1990

Heat flow and boundary value problems for harmonic maps

  • K. C. Chang
  • Ann. Inst. Henri Poincare Anal
  • 1989

On the evolution of harmonic mappings of Riemannian surfaces

  • M. Struwe
  • Commun. Math. Helv
  • 1985
1 Excerpt

Harmonic maps of manifolds with boundary. (Lect

  • R. Hamilton
  • Notes Math.,
  • 1975

The mathematical theory of viscous incompressible flow

  • O. A. Ladyzenskaja
  • (2nd edition) Math. and Appl
  • 1969
1 Excerpt

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