Oscillation waves in Riemann problems inside elliptic regions for conservation laws of mixed type
The authors show that the approximate solutions of the Riemann problem for some systems of conservation laws with the initial data inside an elliptic region may have ``persistent oscillations'', which give rise to new types of measure-valued waves other than shocks and rarefraction waves. They also conclude that ``any local disturbance of a constant state inside the elliptic region will result a nontrivial (distributional or, more generally, measure-valued) solution which is independent of any particular choice of disturbance.'' Two analytical results for testing the convergence of finite difference schemes and for obtaining the expectation values of the state functions respectively, are proved.
scientific article; zbMATH DE number 831613
scientific article