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Citation link: https://nbn-resolving.de/urn:nbn:de:gbv:46-00107730-18
00107730-1.pdf
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Dynamic Inverse Problems for Wave Phenomena


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Other Titles: Dynamische Inverse Probleme für Wellenphänomene
Authors: Gerken, Thies  
Supervisor: Rieder, Andreas 
1. Expert: Rieder, Andreas 
Experts: Schmidt, Alfred
Abstract: 
In this work, we deal with second-order hyperbolic partial differential equations that include time- and space-dependent coefficients, and the inverse problems of identifying these coefficients based on their effect on the equationa s solution. We present the needed theory for such equations, including some regularity results for their solution. This allows to state and analyze the inverse problems, even in an abstract setting where time-dependent operators are sought. Subsequently, we show how these results can be applied to actual partial differential equations. We give a detailed demonstration in the context of the acoustic wave equation. Our results allow the identification of a time- and space-dependent wave speed and mass density in such a setting, and we give an extensive numerical analysis for this case. We also outline how the abstract framework can be applied to other equations, like simple models for electromagnetic waves.
Keywords: inverse problems; evolution equations; wave equation; dynamic inverse problems; time-dependent parameters; elastic wave equation; electrodynamics; ill-posedness
Issue Date: 7-Oct-2019
Type: Dissertation
Secondary publication: no
URN: urn:nbn:de:gbv:46-00107730-18
Institution: Universität Bremen 
Faculty: Fachbereich 03: Mathematik/Informatik (FB 03) 
Appears in Collections:Dissertationen

  

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