  It is known that periodic forcing of nonlinear flows can result in a chaotic
response under certain conditions. Such non-periodic and chaotic solutions have
been observed in simulations of heterogeneous gas flow in a pipeline with
periodic, time-varying boundary conditions. In this paper, we examine a
proportional feedback law for boundary control of a parabolic partial
differential equation system that represents the flow of two gases through a
pipe. We demonstrate that periodic variation of the mass fraction of the
lighter gas at the pipe inlet can result in the chaotic propagation of gas
pressure waves, and show that appropriate flow control can suppress this
response. We examine phase space solutions for the single pipe system subject
to boundary control, and use numerical experiments to characterize conditions
for the controller gain to suppress chaos.
