A viscosity approximation to a system of conservation laws with no classical Riemann solution

  • Barbara Lee Keyfitz
  • Herbert C. Kranzer
Hyperbolic P.D.E. Theory

DOI: 10.1007/BFb0083875

Part of the Lecture Notes in Mathematics book series (LNM, volume 1402)
Cite this paper as:
Keyfitz B.L., Kranzer H.C. (1989) A viscosity approximation to a system of conservation laws with no classical Riemann solution. In: Carasso C., Charrier P., Hanouzet B., Joly JL. (eds) Nonlinear Hyperbolic Problems. Lecture Notes in Mathematics, vol 1402. Springer, Berlin, Heidelberg

Abstract

There are examples of systems of conservation laws which are strictly hyperbolic and genuinely nonlinear but for which the Riemann problem can be solved only for states which are sufficiently close together. For one such example, we introduce a particular type of artificial viscosity and show how it suggests a possible definition of "generalized" solution to the Riemann problem.

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Barbara Lee Keyfitz
    • 1
  • Herbert C. Kranzer
    • 2
  1. 1.Department of MathematicsUniversity of HoustonHouston
  2. 2.Department of MathematicsAdelphi UniversityGarden City

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