Hyperbolic P.D.E. Theory

Nonlinear Hyperbolic Problems

Volume 1402 of the series Lecture Notes in Mathematics pp 185-197


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

  • Barbara Lee KeyfitzAffiliated withDepartment of Mathematics, University of Houston
  • , Herbert C. KranzerAffiliated withDepartment of Mathematics, Adelphi University

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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.