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

Gugat M, Habermann J, Hintermüller M, Huber O (2023)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2023

Journal

European Journal of Applied Mathematics Cambridge University Press

Pages Range: 1-22

URI: https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/abs/constrained-exact-boundary-controllability-of-a-semilinear-model-for-pipeline-gas-flow/FD1A8672AEC80D0C3CA20780787E45A7

DOI: 10.1017/S0956792522000389

Open Access Link: https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/constrained-exact-boundary-controllability-of-a-semilinear-model-for-pipeline-gas-flow/FD1A8672AEC80D0C3CA20780787E45A7

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.

Authors with CRIS profile

Martin Gugat Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Jens Habermann Department of Data Science

Involved external institutions

Humboldt-Universität zu Berlin DE Germany (DE) Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) - Leibniz-Institut im Forschungsverbund Berlin e. V. DE Germany (DE)

How to cite

APA:

Gugat, M., Habermann, J., Hintermüller, M., & Huber, O. (2023). Constrained exact boundary controllability of a semilinear model for pipeline gas flow. European Journal of Applied Mathematics, 1-22. https://dx.doi.org/10.1017/S0956792522000389

MLA:

Gugat, Martin, et al. "Constrained exact boundary controllability of a semilinear model for pipeline gas flow." European Journal of Applied Mathematics (2023): 1-22.

BibTeX: Download