Explicit generalized solutions to a system of conservation laws Article

Received: 27 January 1999 Revised: 07 April 1999 DOI :
10.1007/BF02838000

Cite this article as: Joseph, K.T. Proc. Indian Acad. Sci. (Math. Sci.) (1999) 109: 401. doi:10.1007/BF02838000
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.

Keywords Conservation laws Colombeau algebra generalized solutions

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© Indian Academy of Sciences 1999

Authors and Affiliations 1. School of Mathematics Tata Institute of Fundamental Research Mumbai India