Article Contents
Article Contents

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

• 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.
Mathematics Subject Classification: 35R35.

 Citation: