UNIQUENESS RESULTS FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LARGE AND MONOTONE DATA

We study the uniqueness of solutions to diagonal hyperbolic systems in one spatial dimension and we present two uniqueness results. First, we establish a global existence and uniqueness theorem for continuous solutions to strictly hyperbolic systems. Second, we establish a global existence and uniqu...

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Bibliographic Details
Published in:Journal of hyperbolic differential equations 2013-09, Vol.10 (3), p.461-494
Main Authors: EL HAJJ, AHMAD, MONNEAU, RÉGIS
Format: Article
Language:English
Subjects:
Analysis of PDEs
Existence theorems
Gas dynamics
Hyperbolic differential equations
Hyperbolic systems
Mathematics
Uniqueness
Uniqueness theorems
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Summary:We study the uniqueness of solutions to diagonal hyperbolic systems in one spatial dimension and we present two uniqueness results. First, we establish a global existence and uniqueness theorem for continuous solutions to strictly hyperbolic systems. Second, we establish a global existence and uniqueness theorem for Lipschitz continuous solutions to hyperbolic systems that need not be strictly hyperbolic. Furthermore, an application is presented for one-dimensional flows in isentropic gas dynamics.
ISSN:0219-8916
1793-6993
DOI:10.1142/S0219891613500161