  The analysis and boundary optimal control of the nonlinear transport of gas
on a network of pipelines is considered. The evolution of the gas distribution
on a given pipe is modeled by an isothermal semilinear compressible Euler
system in one space dimension. On the network, solutions satisfying (at nodes)
the so called Kirchhoff flux continuity conditions are shown to exist in a
neighborhood of an equilibrium state. The associated nonlinear optimization
problem then aims at steering such dynamics to a given target distribution by
means of suitable (network) boundary controls while keeping the distribution
within given (state) constraints. The existence of local optimal controls is
established and a corresponding Karush-Kuhn-Tucker (KKT) stationarity system
with an almost surely non-singular Lagrange multiplier is derived.
