Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems

• Main Authors: Bellassoued, Mourad (Author), Yamamoto, Masahiro (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Tokyo : Springer Japan : Imprint: Springer, 2017.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Functional analysis.; Partial differential equations.; Differential geometry.; Manifolds (Mathematics).; Complex manifolds.; Mathematical physics.; Partial Differential Equations.; Functional Analysis.; Differential Geometry.; Manifolds and Cell Complexes (incl. Diff.Topology).; Mathematical Physics.

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...

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.