Hajian, Soheil and Hintermüller, Michael and Schillings, Claudia and Strogtes, Michael
(2018)
*A Bayesian approach to parameter identification in gas networks.*
Preprint : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2537
.

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Official URL: https://www.wias-berlin.de/publications/wias-publ/...

## Abstract

The inverse problem of identifying the friction coefficient in an isothermal semilinear Euler system is considered. Adopting a Bayesian approach, the goal is to identify the distribution of the quantity of interest based on a finite number of noisy measurements of the pressure at the boundaries of the domain. First well-posedness of the underlying non-linear PDE system is shown using semigroup theory, and then Lipschitz continuity of the solution operator with respect to the friction coefficient is established. Based on the Lipschitz property, well-posedness of the resulting Bayesian inverse problem for the identification of the friction coefficient is inferred. Numerical tests for scalar and distributed parameters are performed to validate the theoretical results. Key words.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics > Deterministic and Stochastic PDEs Group |

ID Code: | 2994 |

Deposited By: | Ulrike Eickers |

Deposited On: | 05 Jun 2023 12:39 |

Last Modified: | 05 Jun 2023 12:39 |

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