Inverse Problems and Carleman Estimates:Global Uniqueness, Global Convergence and Experimental Data (Inverse and Ill-Posed Problems Series, 63)

by: Michael V. Klibanov (Author),Jingzhi Li(Author)

Publisher: De Gruyter

Edition: 1st

Publication Date: 2021/9/7

Language: English

Print Length: 344 pages

ISBN-10: 3110745410

ISBN-13: 9783110745412

Book Description

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 for both linear and quasilinear PDEs. Next, various versions of the convexification method are developed for a number of Coefficient Inverse Problems.

About the Author

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 for both linear and quasilinear PDEs. Next, various versions of the convexification method are developed for a number of Coefficient Inverse Problems.

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