Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems

Is based on elementary calculus
Provides direct proof of Carleman estimates
Is one of the few monographs on the approach using Carleman estimates

Is based on elementary calculus Provides direct proof of Carleman estimates Is one of the few monographs on the approach using Carleman estimates Includes supplementary material: sn.pub/extras

Inhalt

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.