Introduction to Inverse Problems for Evolution Equations
Stability and Uniqueness by Carleman Estimates
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Beschreibung
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.
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.
Accessible accounts: needed knowledge is calculus at undergraduate level Self-containedness Applications to inverse problems: unified approach staring with the derivation of Carleman estimates
Autor*in
Masahiro Yamamoto
Themen in »Introduction to Inverse Problems for Evolution Equations«
Inverse Problems for Evolution Equations Single Measurements Uniqueness Stability Carleman Estimate First-Order Transport Equation Parabolic Equation Hyperbolic Equation Elliptic Equation Tikhonov Regularization