  We are concerned with isentropic gas flow in the Laval nozzle with a friction
due to viscosity. It is well known that the flow attains the sonic state at the
throat, where the cross section is minimum in the Laval nozzle. However, the
present friction changes the position of the sonic state into downstream, which
is called chooking. Our goal in this paper is to investigate this phenomena
mathematically.
  From the mathematical point of view, the friction is different from normal
frictions and difficult to treat with. In spite of its physical importance, the
friction has not received much attention until now. For the case without
friction, the global existence of a solution was obtained by author. However,
for the case with the friction, there are only restrictive results. The most
difficult point is to obtain the bounded estimate of solutions. To solve this
problem, we introduce an invariant region depending on the mass. Adjusting the
invariant region, we invent a new difference scheme, which yields approximate
solutions including the mass.
