Introduction to inverse problems for evolution equations : stability and uniqueness by Carleman estimates
Yamamoto, Masahiro
Introduction to inverse problems for evolution equations : stability and uniqueness by Carleman estimates - Cham : Springer, 2025. - xv, 286 pages : illustrations (11 b/w illustrations, 12 illustrations in colour) ; 24 cm. - Lecture notes of the Unione Matematica Italiana ; 29 .
Includes bibliographical references and index.
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.
9783031862663
Carleman theorem
Inverse problems (Differential equations)
Parabolic equation
Hyperbolic equation
Tikhonov regularization
517.972.7 / YAM-I
Introduction to inverse problems for evolution equations : stability and uniqueness by Carleman estimates - Cham : Springer, 2025. - xv, 286 pages : illustrations (11 b/w illustrations, 12 illustrations in colour) ; 24 cm. - Lecture notes of the Unione Matematica Italiana ; 29 .
Includes bibliographical references and index.
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.
9783031862663
Carleman theorem
Inverse problems (Differential equations)
Parabolic equation
Hyperbolic equation
Tikhonov regularization
517.972.7 / YAM-I
