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Introduction to inverse problems for evolution equations = stability and uniqueness by Carleman estimates /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Introduction to inverse problems for evolution equations/ by Masahiro Yamamoto.
Reminder of title:	stability and uniqueness by Carleman estimates /
Author:	Yamamoto, Masahiro.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xv, 287 p. :ill., digital ;24 cm.
[NT 15003449]:	- 1. How inverse problems appear and what should we study about inverse problems? -- 2. Application of the multiplier method to an inverse wave source problem -- 3. Inverse problems by Carleman estimates for first-order transport equations -- 4. Inverse problems by Carleman estimates for parabolic equations -- 5. Inverse problems by Carleman estimates for hyperbolic equations -- 6. Conditional stability and convergence rates of the Tikhonov regularization -- 7. Other estimates of Carleman type -- 8. Derivation of Carleman estimates for elliptic equations.
Contained By:	Springer Nature eBook
Subject:	Inverse problems (Differential equations) -
Online resource:	https://doi.org/10.1007/978-3-031-86267-0
ISBN:	9783031862670

Introduction to inverse problems for evolution equations = stability and uniqueness by Carleman estimates /
Yamamoto, Masahiro.

Introduction to inverse problems for evolution equationsstability and uniqueness by Carleman estimates /[electronic resource] :by Masahiro Yamamoto. - Cham :Springer Nature Switzerland :2025. - xv, 287 p. :ill., digital ;24 cm. - Lecture notes of the Unione Matematica Italiana,291862-9121 ;. - Lecture notes of the Unione Matematica Italiana ;29..

- 1. How inverse problems appear and what should we study about inverse problems? -- 2. Application of the multiplier method to an inverse wave source problem -- 3. Inverse problems by Carleman estimates for first-order transport equations -- 4. Inverse problems by Carleman estimates for parabolic equations -- 5. Inverse problems by Carleman estimates for hyperbolic equations -- 6. Conditional stability and convergence rates of the Tikhonov regularization -- 7. Other estimates of Carleman type -- 8. Derivation of Carleman estimates for elliptic equations.

Among several main formulations, the book treats inverse problems with single measurements by Carleman estimates and describes a method for proving the uniqueness and the stability for the first-order transport equations, parabolic equations, and hyperbolic equations. The book gives self-contained derivations of Carleman estimates, which do not rely on any general theory and simplified application method of the Carleman estimates to the inverse problems. Thus, the target audience is graduate students of faculty of sciences and interested graduate students from engineering fields. The book tries to limit the preliminary knowledge to a standard 4-year undergraduate course. In order to master the methodology, we restrict equations within first-order transport equations, parabolic equations and hyperbolic equations, but it is expected to apply the same methods for other evolution equations such as fluid dynamics.

ISBN: 9783031862670

Standard No.: 10.1007/978-3-031-86267-0doiSubjects--Topical Terms:

566558
Inverse problems (Differential equations)

LC Class. No.: QA371

Dewey Class. No.: 515.357

Introduction to inverse problems for evolution equations = stability and uniqueness by Carleman estimates /
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490 1 $a Lecture notes of the Unione Matematica Italiana, $x 1862-9121 ; $v 29
505 0 $a - 1. How inverse problems appear and what should we study about inverse problems? -- 2. Application of the multiplier method to an inverse wave source problem -- 3. Inverse problems by Carleman estimates for first-order transport equations -- 4. Inverse problems by Carleman estimates for parabolic equations -- 5. Inverse problems by Carleman estimates for hyperbolic equations -- 6. Conditional stability and convergence rates of the Tikhonov regularization -- 7. Other estimates of Carleman type -- 8. Derivation of Carleman estimates for elliptic equations.
520 $a Among several main formulations, the book treats inverse problems with single measurements by Carleman estimates and describes a method for proving the uniqueness and the stability for the first-order transport equations, parabolic equations, and hyperbolic equations. The book gives self-contained derivations of Carleman estimates, which do not rely on any general theory and simplified application method of the Carleman estimates to the inverse problems. Thus, the target audience is graduate students of faculty of sciences and interested graduate students from engineering fields. The book tries to limit the preliminary knowledge to a standard 4-year undergraduate course. In order to master the methodology, we restrict equations within first-order transport equations, parabolic equations and hyperbolic equations, but it is expected to apply the same methods for other evolution equations such as fluid dynamics.
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950 $a Mathematics and Statistics (SpringerNature-11649)