THE RIEMAN PROBLEM FOR THE MAIN MODEL CASES OF THE EULER-POISSON EQUATIONS

We consider the Riemann problem for an inhomogeneous nonstrictly hyperbolic system Vt +VVx =−kE, Et +VEx =n_{0}V, which is a corollary of the Euler–Poisson equations without pressure. The density is found from n = n_{0} −Ex. These equations can be considered for the cases of attractive and repulsive forces as well as for the cases of zero and nonzero underlying density background. The solution to the Riemann problem for each case is nonstandard and contains a delta-shaped singularity in the density component.