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.
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This work was supported by FCT, PEst-OE/MAT/UI0209/2013.
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Sarrico, C.O.R. The Brio system with initial conditions involving Dirac masses: A result afforded by a distributional product. Chin. Ann. Math. Ser. B 35, 941–954 (2014). https://doi.org/10.1007/s11401-014-0862-8
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DOI: https://doi.org/10.1007/s11401-014-0862-8