Proceedings of the Indian Academy of Sciences - Mathematical Sciences

, Volume 109, Issue 4, pp 401–409

Explicit generalized solutions to a system of conservation laws

  • K. T. Joseph

DOI: 10.1007/BF02838000

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


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.


Conservation lawsColombeau algebrageneralized solutions

Copyright information

© Indian Academy of Sciences 1999

Authors and Affiliations

  • K. T. Joseph
    • 1
  1. 1.School of MathematicsTata Institute of Fundamental ResearchMumbaiIndia