Global existence and uniqueness for a hyperbolic system with free boundary

Tong Yang; Fahuai Yi

doi:10.3934/dcds.2001.7.763

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2001, Volume 7, Issue 4: 763-780. Doi: 10.3934/dcds.2001.7.763

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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
2.
Department of Mathematics, South China Normal University, Guangzhou 510631

Received: November 30, 2000

Revised: May 31, 2001

Published: September 2001

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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.

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Mathematics Subject Classification: 35R35.

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