Global existence and uniqueness for a hyperbolic system with free boundary
Tong Yang - Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, 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.
Received: December 2000; Revised: June 2001; Published: July 2001.
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