The Brio system with initial conditions involving Dirac masses: A result afforded by a distributional product
- 51 Downloads
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.
KeywordsProducts of distributions Brio’s system δ-Shock waves δ′-Shock waves Riemann problem
2000 MR Subject Classification46F10 35D
Unable to display preview. Download preview PDF.
- Brio, M., Admissibility conditions for weak solutions of nonstrictly hyperbolic systems, Proc. Int. Conf. on Hyperbolic Problems, Springer-Verlag, Berlin, 1988.Google Scholar
- Korchinski, C., Solution of a Riemann problem for a 2 × 2 system of conservation laws possessing no classical weak solutions, Ph.D. Thesis, Adelphi University, 1977.Google Scholar
- Maslov, V. P. and Tsupin, V. A., Necessary conditions for existence of infinitely narrow solitons in gas dynamics, Soviet Phys. Dock, 24(5), 1979, 354–356.Google Scholar
- Sarrico, C. O. R., The Riemann problem for the Brio system: A solution containing a Dirac mass obtained via a distributional product, submitted.Google Scholar