Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Global existence to the Cauchy problem for hyperbolic conservation laws with an isolated umbilic point


Authors: Elisabetta Felaco, Bruno Rubino and Rosella Sampalmieri
Journal: Quart. Appl. Math. 71 (2013), 629-659
MSC (2010): Primary 35L65, 35L80
DOI: https://doi.org/10.1090/S0033-569X-2013-01328-6
Published electronically: August 28, 2013
MathSciNet review: 3136988
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper the existence of global weak solutions for a $ 2 \times 2$ system of non-strictly hyperbolic non-linear conservation laws is established for data in $ L^{\infty }$.

The result is proven by means of viscous approximation and application of the compensated compactness method.

The presence of a degeneracy in the hyperbolicity of the system requires a careful analysis of the entropy functions, whose regularity is necessary to obtain an existence result. For this purpose we combine the classical techniques referring to a singular Euler-Poisson-Darboux equation with the compensated compactness method.


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Additional Information

Elisabetta Felaco
Affiliation: Department of Mathematics, University of Hamburg, Bundesstrasse 55 Hamburg, 20146, Germany
Email: elisabetta.felaco@math.uni-hamburg.de

Bruno Rubino
Affiliation: Department of Mathematics, University of L’Aquila, via Vetoio 1, L’Aquila, 67100, Italy
Email: rubino@ing.univaq.it

Rosella Sampalmieri
Affiliation: Department of Mathematics, University of L’Aquila, via Vetoio 1, L’Aquila, 67100, Italy
Email: sampalm@ing.univaq.it

DOI: https://doi.org/10.1090/S0033-569X-2013-01328-6
Received by editor(s): October 4, 2011
Received by editor(s) in revised form: March 27, 2012
Published electronically: August 28, 2013
Article copyright: © Copyright 2013 Brown University

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