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

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

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