Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems. 1st ed. 2017

種類:

電子ブック

責任表示:

by Mourad Bellassoued, Masahiro Yamamoto

出版情報:

Tokyo : Springer Japan : Imprint: Springer, 2017

著者名:

• Bellassoued, Mourad.
• Yamamoto, Masahiro.
• SpringerLink (Online service)

シリーズ名:

Springer Monographs in Mathematics ;

ISBN:

9784431566007 [4431566007]    

注記:

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.
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 maps and can often prove the global uniqueness and Lipschitz stability even with a single measurement. These types of inverse problems include coefficient inverse problems of determining physical parameters in inhomogeneous media that appear in many applications related to electromagnetism, elasticity, and related phenomena. Although the methodology was created in 1981 by Bukhgeim and Klibanov, its comprehensive development has been accomplished only recently. In spite of the wide applicability of the method, there are few monographs focusing on combined accounts of Carleman estimates and applications to inverse problems. The aim in this book is to fill that gap. The basic tool is Carleman estimates, the theory of wh

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