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

Submission Status:under review
  • 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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Metadaten
Author:Martin Gugat, Jens Habermann, Michael Hintermüller, Olivier Huber
Document Type:Preprint
Language:English
Date of Publication (online):2021/05/18
Date of first Publication:2021/05/18
Release Date:2021/05/18
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik
Subprojects:B02
C03
C05
C07
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International