LEADER 04327nam 2200577 450 001 9910495229903321 005 20230616193652.0 010 $a3-030-79427-X 024 7 $a10.1007/978-3-030-79427-9 035 $a(CKB)4100000011994624 035 $a(DE-He213)978-3-030-79427-9 035 $a(MiAaPQ)EBC6688940 035 $a(Au-PeEL)EBL6688940 035 $a(PPN)257357114 035 $a(EXLCZ)994100000011994624 100 $a20220415d2021 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntroduction to inverse problems for differential equations /$fAlemdar Hasanov Hasanog?lu, Vladimir G. Romanov 205 $aSecond edition. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (XVII, 515 p. 28 illus., 5 illus. in color.) 311 $a3-030-79426-1 320 $aIncludes bibliographical references and index. 327 $aIntroduction: 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. 330 $aThis 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. For the second edition, the authors have added two new chapters focusing on real-world applications of inverse problems arising in wave and vibration phenomena. They have also revised the whole text of the first edition. 606 $aInverse problems (Differential equations) 606 $aComputer science$xMathematics 606 $aProblemes inversos (Equacions diferencials)$2thub 606 $aEquacions en derivades parcials$2thub 606 $aAnàlisi numèrica$2thub 608 $aLlibres electrònics$2thub 615 0$aInverse problems (Differential equations) 615 0$aComputer science$xMathematics. 615 7$aProblemes inversos (Equacions diferencials) 615 7$aEquacions en derivades parcials 615 7$aAnàlisi numèrica 676 $a515.357 700 $aHasanog?lu$b Alemdar Hasanov$01222243 702 $aRomanov$b Vladimir G. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910495229903321 996 $aIntroduction to inverse problems for differential equations$92834299 997 $aUNINA