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

Rinaldo M. Colombo; Francesca Marcellini; Rinaldo M. Colombo; Francesca Marcellini

doi:10.3934/nhm.2010.5.675

Networks and Heterogeneous Media

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

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

Rinaldo M. Colombo ^{1
,},
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: 01 November 2009 Revised: 01 May 2010
Primary: 35L65; secondary: 76N10.

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.
- Conservation Laws at Junctions,
- Coupling Conditions at Junctions
Citation: Rinaldo M. Colombo, Francesca Marcellini. Coupling conditions for the $3\times 3$ Euler system[J]. Networks and Heterogeneous Media, 2010, 5(4): 675-690. doi: 10.3934/nhm.2010.5.675

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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.

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