Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems
This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions. The formulation is different from that of Dirichlet-to-Neumann ma...
| Main Authors: | , |
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| Language: | English |
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Tokyo :
Springer Japan : Imprint: Springer,
2017.
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| Edition: | 1st ed. 2017. |
| Series: | Springer Monographs in Mathematics,
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| Subjects: | |
| Online Access: | https://doi.org/10.1007/978-4-431-56600-7 |
Table of Contents:
- 1. Basics of Carleman estimates
- 2. Basic tools of Riemannian geometry
- 3. Well-posedness and regularity of the wave equation with variable coefficients
- 4. Carleman estimate of the wave equation in a Riemannian manifold
- 5. Inverse problem and Exact controllability for the wave equation in a Riemannian manifold
- 6. Carleman estimates for some thermoelasticity systems
- 7. Inverse heat source problem for the thermoelasticity system with variable coefficients
- 8. New realization of the pseudoconvexity
- 9. Stability in an inverse problem for a hyperbolic equation with a finite set of boundary data
- 10. Global Carleman estimate for the Laplace-Beltrami operator with an extra elliptic variable and applications.