  We consider the Euler equations for compressible fluids in a nozzle whose
cross-section is variable and may contain discontinuities. We view these
equations as a hyperbolic system in nonconservative form and investigate weak
solutions in the sense of Dal Maso, LeFloch, and Murat. Observing that the
entropy equality has a fully conservative form, we derive a minimum entropy
principle satisfied by entropy solutions. We then establish the stability of a
class of numerical approximations for this system.
