Introduction to Inverse Problems for Differential Equations. 1st ed. 2017

種類:

電子ブック

責任表示:

by Alemdar Hasanov Hasanoğlu, Vladimir G. Romanov

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Hasanov Hasanoğlu, Alemdar.
• Romanov, Vladimir G.
• SpringerLink (Online service)

ISBN:

9783319627977 [331962797X]    

注記:

Introduction: Ill-Posedness of Inverse Problems for Differential and Integral Equations -- PART I. INTRODUCTION TO INVERSE PROBLEMS: 1. Functional Analysis Background of Ill-Posed Problems -- 2. Inverse Source Problems With Final Overdetermination -- PART II. INVERSE PROBLEMS FOR DIFFERENTIAL EQUATIONS: 3. Inverse Problems for Hyperbolic Equations -- 4. One-dimensional Inverse Problems for Electrodynamics Equations -- 5. Inverse Problems for Parabolic Equations -- 6. Inverse Problems for Elliptic Equations -- 7. Inverse Problems for the Stationary Transport Equations -- 8. The Inverse Kinematic Problem -- Appendix A: Invertibility of Linear Operators -- Appendix B: Some Estimates For One-dimensional Parabolic Equation -- Bibliography -- Index.
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

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