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Phase transitions in hyperbolic conservation laws
by
Rinaldo M. Colombo
Department of Mathematics - Brescia University
An increasing quantity of phenomena is being classified under the terms Phase Transition. Conservation laws provide models for several of these phenomena. The present talk is concerned with recent results related to systems of hyperbolic conservation laws that develop phase transitions.
More precisely, we will consider
First, a classical model of a two-phase fluid will be briefly considered. It is well known that suitable admissibility conditions are necessary to single out a unique solution to Riemann Problems. Usually, these conditions are chosen a priori thanks to physical considerations. On the contrary, we will select a posteriori those conditions that lead to well posed problems.
Secondly, a combustion model is considered. Here, the combustion front is sonic with respect to the unburnt gas. A unique solution to the Riemann Problem is selected without the introduction of any admissibility condition. This Riemann solver leads to an existence result for the corresponding Cauchy Problem.
Finally, we consider phase transitions in traffic flow, as recently highlighted in the specialized literature. We propose a new model that provides a description for the transitions from free to congested flow. This model consists of a scalar conservation law coupled with a 2×2 system of conservation laws. The whole is proved to be well posed. Furthermore, it is consistent with various qualitative behaviors of real traffic flow.
Date received: May 31, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cahs-51.