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Global Carleman estimates for degenerate parabolic operators with applications /
Degenerate parabolic operators have received increasing attention in recent years because they are associated with both important theoretical analysis, such as stochastic diffusion processes, and interesting applications to engineering, physics, biology, and economics. This manuscript has been conce...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2016.
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| Colección: | Memoirs of the American Mathematical Society,
no. 1133 |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Chapter 1. Introduction Chapter 2. Controllability and inverse source problems: Notation and main results Chapter 3. Global Carleman estimates for weakly degenerate operators Chapter 4. Some Hardy-type inequalities (proof of Lemma 3.18) Chapter 5. Asymptotic properties of elements of $H^2 (\Omega) \cap H^1 _{A,0}(\Omega)$ Chapter 6. Proof of the topological lemma 3.21 Chapter 7. Outlines of the proof of Theorems 3.23 and 3.26 Chapter 8. Step 1: computation of the scalar product on subdomains (proof of Lemmas 7.1 and 7.16) Chapter 9. Step 2: a first estimate of the scalar product: proof of Lemmas 7.2, 7.4, 7.18 and 7.19 Chapter 10. Step 3: the limits as $\Omega ^\delta \to \Omega $ (proof of Lemmas 7.5 and 7.20) Chapter 11. Step 4: partial Carleman estimate (proof of Lemmas 7.6 and 7.21) Chapter 12. Step 5: from the partial to the global Carleman estimate (proof of Lemmas 7.9-7.11) Chapter 13. Step 6: global Carleman estimate (proof of Lemmas 7.12, 7.14 and 7.15) Chapter 14. Proof of observability and controllability results Chapter 15. Application to some inverse source problems: proof of Theorems 2.9 and 2.11 Chapter 16. Controllability and inverse source problems: notation and main results Chapter 17. Global Carleman estimates for strongly degenerate operators Chapter 18. Hardy-type inequalities: proof of Lemma 17.10 and applications Chapter 19. Global Carleman estimates in the strongly degenerate case: proof of Theorem 17.7 Chapter 20. Proof of Theorem 17.6 (observability inequality) Chapter 21. Lack of null controllability when $\alpha \geq 2$: proof of Proposition 16.5 Chapter 22. Explosion of the controllability cost as $\alpha \to 2^-$ in space dimension $1$: proof of Proposition 16.7 Chapter 23. Some open problems.