Introduction to Inverse Problems for Differential Equations

  • Alemdar Hasanov Hasanoğlu
  • Vladimir G. Romanov

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov
    Pages 1-19
  3. Introduction to Inverse Problems

    1. Front Matter
      Pages 21-21
    2. Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov
      Pages 23-62
    3. Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov
      Pages 63-119
  4. Inverse Problems for Differential Equations

    1. Front Matter
      Pages 121-121
    2. Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov
      Pages 123-143
    3. Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov
      Pages 145-162
    4. Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov
      Pages 163-203
    5. Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov
      Pages 205-218
    6. Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov
      Pages 219-225
    7. Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov
      Pages 227-237
  5. Back Matter
    Pages 239-261

About this book

Introduction

This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering.

The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations.

In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties.

Keywords

inverse problems inverse coefficient problems source problems gradient methods ill-posed problems

Authors and affiliations

  • Alemdar Hasanov Hasanoğlu
    • 1
  • Vladimir G. Romanov
    • 2
  1. 1.Department of MathematicsUniversity of KocaeliIzmitTurkey
  2. 2.Sobolev Institute of MathematicsNovosibirskRussia

Bibliographic information