Global existence and uniqueness for a hyperbolic system with free boundary

Tong Yang; Fahuai Yi

doi:10.3934/dcds.2001.7.763

Global existence and uniqueness for a hyperbolic system with free boundary

Tong Yang, Fahuai Yi

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

5 Citations (Scopus)

Abstract

In this paper, we consider a 2 x 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.

Original language	English
Pages (from-to)	763-780
Journal	Discrete and Continuous Dynamical Systems
Volume	7
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2001.7.763
Publication status	Published - 2001

Research Keywords

Classical solution
Hyperbolic system
Stefan problem

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abstract = "In this paper, we consider a 2 x 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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T1 - Global existence and uniqueness for a hyperbolic system with free boundary

AU - Yang, Tong

AU - Yi, Fahuai

PY - 2001

Y1 - 2001

N2 - In this paper, we consider a 2 x 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.

AB - In this paper, we consider a 2 x 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.

KW - Classical solution

KW - Hyperbolic system

KW - Stefan problem

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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0035615437&origin=recordpage

U2 - 10.3934/dcds.2001.7.763

DO - 10.3934/dcds.2001.7.763

M3 - RGC 21 - Publication in refereed journal

SN - 1078-0947

VL - 7

SP - 763

EP - 780

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 4

ER -

Global existence and uniqueness for a hyperbolic system with free boundary

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Research Keywords

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