This work focuses on the Riemann problem of Euler equations with global
constant initial conditions and a single-point heating source, which
comes from the physical problem of heating one-dimensional inviscid
compressible constant flow. In order to deal with the source of Dirac
delta-function, we propose an analytical frame of double classic Riemann
problems(CRPs) coupling, which treats the fluids on both sides of the
heating point as two separate Riemann problems and then couples them.
Three structures of the exact Riemann solution are found, which is
consistent with the results of numerical methods. Furthermore, we
establish the uniqueness of the Riemann solution with some restrictions
on the Mach number of the initial condition.