  In this paper, we study the global existence and asymptotic behavior of
classical solutions near vacuum for the initial-boundary value problem modeling
isentropic supersonic flows through divergent ducts. The governing equations
are the compressible Euler equations with a small parameter, which can be
written as a hyperbolic system in terms of the Riemann invariants with a
non-dissipative source. We provide a new result for the global existence of
classical solutions to initial-boundary value problems of non-dissipative
hyperbolic balance laws without the assumption of small data. The work is based
on the local existence, the maximum principle and the uniform a priori
estimates obtained by the generalized Lax transformations. The asymptotic
behavior of classical solutions is also shown by studying the behavior of
Riemann invariants along each characteristic curve and vertical line. The
results can be applied to the spherically symmetric solutions to N-dimensional
compressible Euler equations. Numerical simulations are provided to support our
theoretical results.
