Introduction to Inverse Problems for Evolution Equations
Stability and Uniqueness by Carleman Estimates
Series: Lecture Notes of the Unione Matematica Italiana; 29;
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Product details:
- Publisher Springer Nature Switzerland
- Date of Publication 31 August 2025
- Number of Volumes 1 pieces, Book
- ISBN 9783031862663
- Binding Paperback
- No. of pages287 pages
- Size 235x155 mm
- Language English
- Illustrations XV, 287 p. 23 illus., 12 illus. in color. 692
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Long description:
"
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.
" MoreTable of Contents:
- 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.
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