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Published in:
An Inverse Conductivity Problem in Multifrequency Electric Impedance Tomography Read chapter Read first chapter

2020 | OriginalPaper | Chapter

6. Inverse Problems for a Compressible Fluid System

Authors : Oleg Yu. Imanuvilov, Masahiro Yamamoto

Published in: Inverse Problems and Related Topics

Publisher: Springer Singapore

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Abstract

In this article, we discuss the methodology based on Carleman estimates   concerning the unique continuation and inverse problems of determining spatially varying coefficients. First as retrospective views we refer to main works by that methodology starting from the pioneering work by Bukhgeim and Klibanov published in 1981. Then as one possible object of the application of this methodology, we start to consider compressible fluid flows and we prove conditional stability estimates for an inverse source problem and the continuation of solutions from a part of lateral boundary. We apply two types of Carleman estimates respectively with a weight function which is quadratic in time and a weight function which rapidly decays at the end points of the time interval.

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previous chapter Inverse Moving Source Problem for Fractional Diffusion(-Wave) Equations: Determination of Orbits
next chapter Carleman Estimate for a General Second-Order Hyperbolic Equation
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Metadata
Title
Inverse Problems for a Compressible Fluid System
Authors
Oleg Yu. Imanuvilov
Masahiro Yamamoto
Copyright Year
2020
Publisher
Springer Singapore
Book
Inverse Problems and Related Topics

Print ISBN: 978-981-15-1591-0

Electronic ISBN: 978-981-15-1592-7

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-981-15-1592-7_6

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