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Parameter identification in a semilinear hyperbolic system

Submission Status:under review
  • We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and con- traction arguments. We then investigte the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a varia- tional regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized so- lutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings

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Metadaten
Author:Herbert Egger, Thomas Kugler, Nikolai Strogies
Parent Title (English):Inverse Problems
Document Type:Article
Language:English
Date of Publication (online):2016/09/16
Date of first Publication:2016/09/16
Release Date:2016/09/16
Volume:33
Issue:055022
Institutes:Technische Universität Darmstadt
Weierstraß-Institut für Angewandte Analysis und Stochastik
Subprojects:B02
C04