Chinese Annals of Mathematics, Series B

, Volume 35, Issue 6, pp 941–954 | Cite as

The Brio system with initial conditions involving Dirac masses: A result afforded by a distributional product

Article

Abstract

The Brio system is a 2 × 2 fully nonlinear system of conservation laws which arises as a simplified model in the study of plasmas. The present paper offers explicit solutions to this system subjected to initial conditions containing Dirac masses. The concept of a solution emerges within the framework of a distributional product and represents a consistent extension of the concept of a classical solution. Among other features, the result shows that the space of measures is not sufficient to contain all solutions of this problem.

Keywords

Products of distributions Brio’s system δ-Shock waves δ′-Shock waves Riemann problem 

2000 MR Subject Classification

46F10 35D 

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Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.CMAFUniversity of LisbonLisboaPortugal

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