Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems

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.

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• Topologia
• Física Matemática
• Cálculo diferencial e equações
• Análise funcional e transforma
• Geometria diferencial e riemaniana

Cauchy problem;Riemannian geometry;coefficient invers problem;conditional stability;hand-made derivation of Carleman estimate;partial differential equations