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Introduction to Inverse Problems for Evolution Equations : Stability and Uniqueness by Carleman Estimates - Masahiro Yamamoto

Introduction to Inverse Problems for Evolution Equations

Stability and Uniqueness by Carleman Estimates

By: Masahiro Yamamoto

eText | 30 August 2025

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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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Non-FictionMathematicsCalculus & Mathematical Analysis

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