Introduction to Inverse Problems for Evolution Equations : Stability and Uniqueness by Carleman Estimates / / by Masahiro Yamamoto
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| Autore: |
Yamamoto Masahiro
|
| Titolo: |
Introduction to Inverse Problems for Evolution Equations : Stability and Uniqueness by Carleman Estimates / / by Masahiro Yamamoto
|
| Pubblicazione: | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025 |
| Edizione: | 1st ed. 2025. |
| Descrizione fisica: | 1 online resource (412 pages) |
| Disciplina: | 515.357 |
| Soggetto topico: | Mathematical analysis |
| Mathematics | |
| Analysis | |
| Nota di contenuto: | - 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. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Introduction to Inverse Problems for Evolution Equations |
| ISBN: | 3-031-86267-8 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9911022453603321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Lecture Notes of the Unione Matematica Italiana, . 1862-9121 ; ; 29