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Abstract
This thesis is concerned with the mathematical analysis of inverse problems for partial diﬀerential equations, and with a speciﬁc type of such problems known as hybrid inverse problems. Chapters 14 present various aspects of the theory of inverse problems for partial diﬀerential equations. Chapters 56 introduce the topic of hybrid inverse problems and content of the scientiﬁc papers in the appendix.
The scientiﬁc papers are concerned with the analysis of hybrid inverse problems. Speciﬁcally, we consider photoacoustic tomography and acoustoelectric tomography, as well as the multifrequency inverse source problem for the Helmholtz equation.
For photoacoustic tomography, we analyze the stability and uniqueness of the inverse problem of reconstructing the optical coeﬃcients of an object in a situation where measurement data is collected by a measurement device that can rotate around the object.
For acoustoelectric tomography, we provide a method to reconstruct the electrical conductivity from boundary measurements of the voltage. Moreover, we investigate the feasibility of acoustoelectric tomography for medical imaging by examining how reconstructions depend on the strength of the acoustoelectric coupling.
In the case of multifrequency measurements of solutions to the Helmholtzequation, we provide a detailed characterization of sources that can be stably reconstructed. The characterization depends on the measurement frequencies, and we devise an eﬀective and stable reconstruction method.
The scientiﬁc papers are concerned with the analysis of hybrid inverse problems. Speciﬁcally, we consider photoacoustic tomography and acoustoelectric tomography, as well as the multifrequency inverse source problem for the Helmholtz equation.
For photoacoustic tomography, we analyze the stability and uniqueness of the inverse problem of reconstructing the optical coeﬃcients of an object in a situation where measurement data is collected by a measurement device that can rotate around the object.
For acoustoelectric tomography, we provide a method to reconstruct the electrical conductivity from boundary measurements of the voltage. Moreover, we investigate the feasibility of acoustoelectric tomography for medical imaging by examining how reconstructions depend on the strength of the acoustoelectric coupling.
In the case of multifrequency measurements of solutions to the Helmholtzequation, we provide a detailed characterization of sources that can be stably reconstructed. The characterization depends on the measurement frequencies, and we devise an eﬀective and stable reconstruction method.
Original language  English 

Publisher  Technical University of Denmark 

Number of pages  182 
Publication status  Published  2019 
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Dive into the research topics of 'On Hybrid Inverse Problems for Partial Diﬀerential Equations'. Together they form a unique fingerprint.Projects
 1 Finished

Mathematical Analysis and Computations for Multiphysics Tomography
Kirkeby, A., Knudsen, K., Evgrafov, A., Karamehmedovic, M., Brander, D., Alberti, G. S. & Grasmair, M.
Technical University of Denmark
15/12/2015 → 11/12/2019
Project: PhD