Vanishing viscosity on a star-shaped graph under general transmission conditions at the node

Giuseppe Maria Coclite; Carlotta Donadello; Giuseppe Maria Coclite; Carlotta Donadello

doi:10.3934/nhm.2020009

Networks and Heterogeneous Media

2020, Volume 15, Issue 2: 197-213. doi: 10.3934/nhm.2020009

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Vanishing viscosity on a star-shaped graph under general transmission conditions at the node

Giuseppe Maria Coclite ^{1
,
,},
Carlotta Donadello ^{2
,}

1.
Department of Mechanics, Mathematics and Management, Polytechnic University of Bari, Via E. Orabona 4, 70125 Bari, Italy
2.
Laboratoire de Mathématiques CNRS UMR6623, Université de Bourgogne Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France

Received: 01 May 2019 Revised: 01 November 2019 Published: 01 June 2020
Primary: 35L65; Secondary: 35R02

In this paper we consider a family of scalar conservation laws defined on an oriented star shaped graph and we study their vanishing viscosity approximations subject to general matching conditions at the node. In particular, we prove the existence of converging subsequence and we show that the limit is a weak solution of the original problem.
- Conservation laws,
- vanishing viscosity,
- networks,
- transmission conditions at nodes
Citation: Giuseppe Maria Coclite, Carlotta Donadello. Vanishing viscosity on a star-shaped graph under general transmission conditions at the node[J]. Networks and Heterogeneous Media, 2020, 15(2): 197-213. doi: 10.3934/nhm.2020009

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Abstract

In this paper we consider a family of scalar conservation laws defined on an oriented star shaped graph and we study their vanishing viscosity approximations subject to general matching conditions at the node. In particular, we prove the existence of converging subsequence and we show that the limit is a weak solution of the original problem.

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