WIAS Preprint No. 2899, (2021)

Constrained exact boundary controllability of a semilinear model for pipeline gas flow



Authors

  • Gugat, Martin
  • Habermann, Jens
  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Huber, Olivier
    ORCID: 0000-0002-4447-8650

2020 Mathematics Subject Classification

  • 93B05 93C10

Keywords

  • Gas pipeline flow, exact controllability, continuous solutions, constrained exact controllability, boundary control, method of characteristics

DOI

10.20347/WIAS.PREPRINT.2899

Abstract

While the quasilinear isothermal Euler equations are an excellent model for gas pipeline flow, the operation of the pipeline flow with high pressure and small Mach numbers allows us to obtain approximate solutions by a simpler semilinear model. We provide a derivation of the semilinear model that shows that the semilinear model is valid for sufficiently low Mach numbers and sufficiently high pressures. We prove an existence result for continuous solutions of the semilinear model that takes into account lower and upper bounds for the pressure and an upper bound for the magnitude of the Mach number of the gas flow. These state constraints are important both in the operation of gas pipelines and to guarantee that the solution remains in the set where the model is physically valid. We show the constrained exact boundary controllability of the system with the same pressure and Mach number constraints.

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