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Explicit generalized solutions to a system of conservation laws

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Abstract

This paper studies a special 3 by 3 system of conservation laws which cannot be solved in the classical distributional sense. By adding a viscosity term and writing the system in the form of a matrix Burgers equation an explicit formula is found for the solution of the pure initial value problem. These regularized solutions are used to construct solutions for the conservation laws with initial conditions, in the algebra of generalized functions of Colombeau. Special cases of this system were studied previously by many authors.

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  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400005, Mumbai, India

    K. T. Joseph

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  1. K. T. Joseph
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Joseph, K.T. Explicit generalized solutions to a system of conservation laws. Proc. Indian Acad. Sci. (Math. Sci.) 109, 401–409 (1999). https://doi.org/10.1007/BF02838000

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  • DOI: https://doi.org/10.1007/BF02838000

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