American Institute of Mathematical Sciences

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

Global existence and uniqueness for a hyperbolic system with free boundary

Tong Yang 1, and  Fahuai Yi 2,

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.
Keywords: Stefan problem, classical solution., Hyperbolic system.
Mathematics Subject Classification: 35R3.
Citation: Tong Yang, Fahuai Yi. Global existence and uniqueness for a hyperbolic system with free boundary. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 763-780. doi: 10.3934/dcds.2001.7.763
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