Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Global existence and uniqueness for a hyperbolic system with free boundary

Pages: 763 - 780, Volume 7, Issue 4, October 2001      doi:10.3934/dcds.2001.7.763

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Tong Yang - Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, China (email)
Fahuai Yi - Department of Mathematics, South China Normal University, Guangzhou 510631, China (email)

Abstract: In this paper, we consider a $2\times 2$ hyperbolic system originates from the theory of phase dynamics. This one-phase problem can be obtained by using the Catteneo-Fourier law which is a variant of the standard Fourier law in one dimensional space. A new classical existence and uniqueness result is established by some a priori estimates using the characteristic method. The convergence of the solutions to the one of classical Stefan problems is also obtained.

Keywords:  Hyperbolic system, Stefan problem, classical solution.
Mathematics Subject Classification:  35R35.

Received: December 2000;      Revised: June 2001;      Available Online: July 2001.