Communications in Mathematical Sciences

Volume 14 (2016)

Number 6

On a limit of perturbed conservation laws with diffusion and non-positive dispersion

Pages: 1501 – 1516

DOI: https://dx.doi.org/10.4310/CMS.2016.v14.n6.a2

Authors

Nabil Bedjaoui (Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, Université de Picardie Jules Verne, Amiens, France)

Joaquim M.C. Correia (DMat, ECT, CIMA, IIFA, Universidade de Évora, Lisbon, Portugal)

Youcef Mammeri (Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, Université de Picardie Jules Verne, Amiens, France )

Abstract

We consider a conservation law perturbed by a linear diffusion and a general form of non-positive dispersion. We prove the convergence of the corresponding solution to the entropy weak solution of the hyperbolic conservation law.

Keywords

diffusion, dispersion, KdV equation, Burgers’ equation, hyperbolic conservation laws, entropy measure-valued solutions

2010 Mathematics Subject Classification

35G25, 35L65, 35Q53, 76B15

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Published 12 August 2016