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Universität Bremen

1. Gerken, Thies. Dynamic Inverse Problems for Wave Phenomena.

Degree: PhD, FB3, 2019, Universität Bremen

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. Advisors/Committee Members: Rieder, Andreas (advisor), Rieder, Andreas (referee), Schmidt, Alfred (referee).

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Gerken, T. (2019). Dynamic Inverse Problems for Wave Phenomena. (Doctoral Dissertation). Universität Bremen. Retrieved from http://elib.suub.uni-bremen.de/edocs/00107730-1.pdf

Chicago Manual of Style (16th Edition):

Gerken, Thies. “Dynamic Inverse Problems for Wave Phenomena.” 2019. Doctoral Dissertation, Universität Bremen. Accessed November 17, 2019. http://elib.suub.uni-bremen.de/edocs/00107730-1.pdf.

MLA Handbook (7th Edition):

Gerken, Thies. “Dynamic Inverse Problems for Wave Phenomena.” 2019. Web. 17 Nov 2019.

Vancouver:

Gerken T. Dynamic Inverse Problems for Wave Phenomena. [Internet] [Doctoral dissertation]. Universität Bremen; 2019. [cited 2019 Nov 17]. Available from: http://elib.suub.uni-bremen.de/edocs/00107730-1.pdf.

Council of Science Editors:

Gerken T. Dynamic Inverse Problems for Wave Phenomena. [Doctoral Dissertation]. Universität Bremen; 2019. Available from: http://elib.suub.uni-bremen.de/edocs/00107730-1.pdf

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