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Inverse problems for abstract evolution equations with applications in electrodynamics and elasticity

Kirsch, Andreas; Rieder, Andreas

Abstract:
It is common knowledge { mainly based on experience { that parameter identification problems in partial differential equations are ill-posed. Yet, a mathematical sound argumentation is missing, except for some special cases. We present a general theory for inverse problems related to abstract evolution equations which explains not only their local ill-posedness but also provides the Fréchet derivative of the corresponding parameter-to-solution map which is needed, e.g., in Newton-like solvers. Our abstract results are applied to inverse problems related to the following first order hyperbolic systems: Maxwell's equation (electromagnetic scattering in conducting media) and elastic wave equation (seismic imaging).


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000051550
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-515509
KITopen ID: 1000051550
Verlag KIT, Karlsruhe
Umfang 21 S.
Serie CRC 1173 ; 2016/1
Schlagworte inverse problems, ill-posed problems, evolution equation, Frechet-differentiability, electrodynamic wave equations, elastic wave equations
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