# American Institute of Mathematical Sciences

October  2001, 7(4): 763-780. doi: 10.3934/dcds.2001.7.763

## Global existence and uniqueness for a hyperbolic system with free boundary

 1 Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, China 2 Department of Mathematics, South China Normal University, Guangzhou 510631, China

Received  December 2000 Revised  June 2001 Published  July 2001

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.
Citation: Tong Yang, Fahuai Yi. Global existence and uniqueness for a hyperbolic system with free boundary. Discrete & Continuous Dynamical Systems, 2001, 7 (4) : 763-780. doi: 10.3934/dcds.2001.7.763
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