  This paper is concerned with the Riemann problem of one-dimensional Euler
equations with a singular source.
  The exact solution of this Riemann problem contains a stationary
discontinuity induced by the singular source, which is different from all the
simple waves in the Riemann solution of classical Euler equations.
  We propose an eigenvalue-based monotonicity criterion to select the physical
curve of this stationary discontinuity.
  By including this stationary discontinuity as an elementary wave, the
structure of Riemann solution becomes diverse, e.g. the number of waves is not
fixed and interactions between two waves become possible.
  Under the double CRP framework, we prove all possible structures of the
Riemann solution.
