Coupling conditions for the $3\times 3$ Euler system

Rinaldo M. Colombo; Francesca Marcellini

doi:10.3934/nhm.2010.5.675

Article Contents

2010, Volume 5, Issue 4: 675-690. Doi: 10.3934/nhm.2010.5.675

This issue Previous Article Next Article Classical solutions and feedback stabilization for the gas flow in a sequence of pipes

Coupling conditions for the $3\times 3$ Euler system

Rinaldo M. Colombo^1, and
Francesca Marcellini^2,

1.
Dipartimento di Matematica, Università degli Studi di Brescia, Via Branze 38, 25123 Brescia
2.
Dipartimento di Matematica e Applicazioni, Università di Milano–Bicocca, Via Cozzi 53, 20126 Milano

Received: October 31, 2009

Revised: April 30, 2010

Published: November 2010

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Abstract

This paper is devoted to the extension to the full $3\times3$ Euler system of the basic analytical properties of the equations governing a fluid flowing in a duct with varying section. First, we consider the Cauchy problem for a pipeline consisting of 2 ducts joined at a junction. Then, this result is extended to more complex pipes. A key assumption in these theorems is the boundedness of the total variation of the pipe's section. We provide explicit examples to show that this bound is necessary.

Keywords:

Conservation Laws at Junctions,
Coupling Conditions at Junctions.

Mathematics Subject Classification: Primary: 35L65; secondary: 76N10.

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References

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