Parameter identification in a semilinear hyperbolic system
- 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
Author: | Herbert Egger, Thomas Kugler, Nikolai Strogies |
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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 |