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

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## 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## Preview

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