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Non-classical global solutions for a class of scalar conservation laws

Published online by Cambridge University Press:  12 July 2007

Paolo Baiti
Paolo Baiti
Affiliation:
Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, Udine 33100, Italy (baiti@dimi.uniud.it)
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Abstract

We consider the Cauchy problem for a class of scalar conservation laws with flux having a single inflection point. We prove existence of global weak solutions satisfying a single entropy inequality together with a kinetic relation, in a class of bounded variation functions. The kinetic relation is obtained by the travelling-wave criterion for a regularization consisting of balanced diffusive and dispersive terms. The result is applied to the one-dimensional Buckley-Leverett equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 2 , April 2004 , pp. 225 - 240
Copyright
Copyright © Royal Society of Edinburgh 2004

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