Inverse Problems and Carleman Estimates : : Global Uniqueness, Global Convergence and Experimental Data /

Inverse Problems and Carleman Estimates : : Global Uniqueness, Global Convergence and Experimental Data / / Michael V. Klibanov, Jingzhi Li.

This book summarizes the main analytical and numerical results of Carleman estimates. In the analytical part, Carleman estimates for three main types of Partial Differential Equations (PDEs) are derived. In the numerical part, first numerical methods are proposed to solve ill-posed Cauchy problems f...

Full description

Saved in:
Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter DG Ebook Package English 2021
VerfasserIn:
Klibanov, Michael V.,
Li, Jingzhi,
Place / Publishing House:Berlin ;, Boston : : De Gruyter, , [2021]
©2021
Year of Publication:2021
Language:English
Series:Inverse and Ill-Posed Problems Series , 63
Online Access:
Physical Description:1 online resource (XVI, 328 p.)
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • Frontmatter
  • 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 L2(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

Similar Items