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A Hölder continuous ODE related to traffic flow

Published online by Cambridge University Press:  12 July 2007

Rinaldo M. Colombo  and
Andrea Marson
Rinaldo M. Colombo
Affiliation:
Department of Mathematics, Via Valotti 9, 25133 Brescia, Italy
Andrea Marson
Affiliation:
Department of Pure and Applied Mathematics, Via Belzoni 7, 35131 Padova, Italy
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Abstract

This paper is devoted to the proof of the well posedness of a class of ordinary differential equations (ODEs). The vector field depends on the solution to a scalar conservation law. Forward uniqueness of Filippov solutions is obtained, as well as their Hölder continuous dependence on the initial data of the ODE. Furthermore, we prove the continuous dependence in C0 of the solution to the ODE from the initial data of the conservation law in L1.

This problem is motivated by a model of traffic flow.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 4 , August 2003 , pp. 759 - 772
Copyright
Copyright © Royal Society of Edinburgh 2003

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