Inverse problems and Carleman estimates : global uniqueness, global convergence and experimental data / Michael V. Klibanov, Jingzhi Li.

Format:

Book

Author/Creator:

Klibanov, M. V. (Michael V.), author.

Li, Jingzhi, 1943- author.

Series:

Inverse and Ill-Posed Problems

Inverse and Ill-Posed Problems ; v.63

Language:

English

Subjects (All):

Inverse problems (Differential equations).

Inverse problems (Differential equations)--Numerical solutions.

Physical Description:

1 online resource (344 pages)

Place of Publication:

Berlin : Walter de Gruyter GmbH, [2021]

Summary:

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Contents:

Intro

Preface

Acknowledgments

Contents

1 Topics of this book

2 Carleman estimates and Hölder stability for ill-posed Cauchy problems

3 Global uniqueness for coefficient inverse problems and Lipschitz stability for a hyperbolic CIP

4 The quasi-reversibility numerical method for ill-posed Cauchy problems for linear PDEs

5 Convexification for ill-posed Cauchy problems for quasi-linear PDEs

6 A special orthonormal basis in L&lt

sub&gt

2&lt

/sub&gt

(a, b) for the convexification for CIPs without the initial conditions-restricted Dirichlet-to-Neumann map

7 Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data

8 Convexification for a coefficient inverse problem for a hyperbolic equation with a single location of the point source

9 Convexification for an inverse parabolic problem

10 Experimental data and convexification for the recovery of the dielectric constants of buried targets using the Helmholtz equation

11 Travel time tomography with formally determined incomplete data in 3D

12 Numerical solution of the linearized travel time tomography problem with incomplete data

Bibliography

Index.

Notes:

Description based on print version record.

ISBN:

3-11-074548-8

OCLC:

1266229373