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Inverse Problems for Fractional Operators Involving a Magnetic Potential.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Inverse Problems for Fractional Operators Involving a Magnetic Potential./
Author:	Li, Li.
Description:	1 online resource (59 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
Contained By:	Dissertations Abstracts International83-02B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28490689click for full text (PQDT)
ISBN:	9798535503134

Inverse Problems for Fractional Operators Involving a Magnetic Potential.
Li, Li.

Inverse Problems for Fractional Operators Involving a Magnetic Potential. - 1 online resource (59 pages)

Source: Dissertations Abstracts International, Volume: 83-02, Section: B.

Thesis (Ph.D.)--University of Washington, 2021.

Includes bibliographical references

In this thesis, we study forward and inverse problems for fractional operators involving a magnetic potential. We show that many properties of fractional operators are preserved under the perturbation by a magnetic potential. Besides, we carefully use Runge approximation properties to obtain strong results when we study inverse problems. More precisely, we determine both the magnetic potential and the electric potential from exterior partial measurements of the Dirichlet-to-Neumann map in the linear fractional inverse problem by using the Runge approximation property and an integral identity; we also determine both the magnetic potential and the non-linearity in the semi-linear fractional inverse problem by using the Runge approximation property and a first order linearization.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798535503134Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Forward and inverse problemsIndex Terms--Genre/Form:

542853
Electronic books.

Inverse Problems for Fractional Operators Involving a Magnetic Potential.
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100 1 $a Li, Li. $3 1036040
245 1 0 $a Inverse Problems for Fractional Operators Involving a Magnetic Potential.
264 0 $c 2021
300 $a 1 online resource (59 pages)
336 $a text $b txt $2 rdacontent
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500 $a Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
500 $a Advisor: Uhlmann, Gunther.
502 $a Thesis (Ph.D.)--University of Washington, 2021.
504 $a Includes bibliographical references
520 $a In this thesis, we study forward and inverse problems for fractional operators involving a magnetic potential. We show that many properties of fractional operators are preserved under the perturbation by a magnetic potential. Besides, we carefully use Runge approximation properties to obtain strong results when we study inverse problems. More precisely, we determine both the magnetic potential and the electric potential from exterior partial measurements of the Dirichlet-to-Neumann map in the linear fractional inverse problem by using the Runge approximation property and an integral identity; we also determine both the magnetic potential and the non-linearity in the semi-linear fractional inverse problem by using the Runge approximation property and a first order linearization.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Electromagnetics. $3 3173223
650 4 $a Mathematical functions. $3 3564295
650 4 $a Approximation. $3 3560410
650 4 $a Partial differential equations. $3 2180177
650 4 $a Banach spaces. $3 579190
650 4 $a Inverse problems. $3 3686950
653 $a Forward and inverse problems
653 $a Fractional operators
653 $a Magnetic potential
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0405
690 $a 0607
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a University of Washington. $b Mathematics. $3 3173597
773 0 $t Dissertations Abstracts International $g 83-02B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28490689 $z click for full text (PQDT)