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Degenerate Hyperbolic Conservation Laws with Dissipation: Reduction to and Validity of a Class of Burgers-Type Equations

Bridges, Thomas, Pennant, J and Zelik, Sergey (2014) Degenerate Hyperbolic Conservation Laws with Dissipation: Reduction to and Validity of a Class of Burgers-Type Equations ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 214 (2). pp. 671-716.

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Abstract

A conservation law is said to be degenerate or critical if the Jacobian of the flux vector evaluated on a constant state has a zero eigenvalue. In this paper, it is proved that a degenerate conservation law with dissipation will generate dynamics on a long time scale that resembles Burger’s dynamics. The case of k-fold degeneracy is also treated, and it is shown that it leads to a reduction to a quadratically coupled k-fold system of Burgers-type equations. Validity of the reduction and existence for the reduced system is proved in the class of uniformly local spaces, thereby capturing both finite and infinite energy solutions. The theory is applied to some examples, from stratified shallow-water hydrodynamics, that model the birth of hydraulic jumps.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Bridges, ThomasT.Bridges@surrey.ac.ukUNSPECIFIED
Pennant, JUNSPECIFIEDUNSPECIFIED
Zelik, SergeyS.Zelik@surrey.ac.ukUNSPECIFIED
Date : 1 November 2014
Identification Number : https://doi.org/10.1007/s00205-014-0772-7
Copyright Disclaimer : © Springer-Verlag Berlin Heidelberg (2014)
Uncontrolled Keywords : Science & Technology, Physical Sciences, Technology, Mathematics, Interdisciplinary Applications, Mechanics, Mathematics, HYDRAULIC EXCHANGE FLOWS, UNBOUNDED-DOMAINS, INVARIANT-MANIFOLDS, SPECTRAL STABILITY, WAVES, ATTRACTORS, SYSTEMS, MODEL, MODULATION
Related URLs :
Additional Information : The original publication is available at http://www.springerlink.com
Depositing User : Symplectic Elements
Date Deposited : 17 Dec 2014 09:47
Last Modified : 30 Jun 2017 13:49
URI: http://epubs.surrey.ac.uk/id/eprint/806825

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