Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems

Softcover Nachdruck of the original 1. Auflage 2017
ISBN: 978-4-431-56830-8
Verlag: Springer

Buch, Englisch, 260 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 417 g

Reihe: Springer Monographs in Mathematics

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

Zielgruppe

Research

Autoren/Hrsg.

Bellassoued, Mourad

Yamamoto, Masahiro

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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.