LEADER 05160nam 2200649 a 450 001 9910465261203321 005 20200520144314.0 010 $a3-11-022401-1 024 7 $a10.1515/9783110224016 035 $a(CKB)2560000000079377 035 $a(EBL)835416 035 $a(OCoLC)772845127 035 $a(SSID)ssj0000591278 035 $a(PQKBManifestationID)11364766 035 $a(PQKBTitleCode)TC0000591278 035 $a(PQKBWorkID)10672012 035 $a(PQKB)11580171 035 $a(MiAaPQ)EBC835416 035 $a(DE-B1597)37948 035 $a(OCoLC)840443947 035 $a(DE-B1597)9783110224016 035 $a(PPN)175536147 035 $a(Au-PeEL)EBL835416 035 $a(CaPaEBR)ebr10527901 035 $a(CaONFJC)MIL628090 035 $a(EXLCZ)992560000000079377 100 $a20110927d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aInverse and ill-posed problems$b[electronic resource] $etheory and applications /$fSergey I. Kabanikhin 210 $aBerlin ;$aBoston $cDe Gruyter$dc2012 215 $a1 online resource (475 p.) 225 1 $aInverse and ill-posed problems series,$x1381-4524 ;$v55 300 $aDescription based upon print version of record. 311 $a1-306-96839-9 311 $a3-11-022400-3 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tPreface / $rKabanikhin, Sergey I. -- $tDenotations -- $tContents -- $tChapter 1. Basic concepts and examples -- $tChapter 2. Ill-posed problems -- $tChapter 3. Ill-posed problems of linear algebra -- $tChapter 4. Integral equations -- $tChapter 5. Integral geometry -- $tChapter 6. Inverse spectral and scattering problems -- $tChapter 7. Linear problems for hyperbolic equations -- $tChapter 8. Linear problems for parabolic equations -- $tChapter 9. Linear problems for elliptic equations -- $tChapter 10. Inverse coefficient problems for hyperbolic equations -- $tChapter 11. Inverse coefficient problems for parabolic and elliptic equations -- $tAppendix A -- $tAppendix B -- $tEpilogue -- $tBibliography -- $tIndex 330 $aThe theory of ill-posed problems originated in an unusual way. As a rule, a new concept is a subject in which its creator takes a keen interest. The concept of ill-posed problems was introduced by Hadamard with the comment that these problems are physically meaningless and not worthy of the attention of serious researchers. Despite Hadamard's pessimistic forecasts, however, his unloved "child" has turned into a powerful theory whose results are used in many fields of pure and applied mathematics. What is the secret of its success? The answer is clear. Ill-posed problems occur everywhere and it is unreasonable to ignore them. Unlike ill-posed problems, inverse problems have no strict mathematical definition. In general, they can be described as the task of recovering a part of the data of a corresponding direct (well-posed) problem from information about its solution. Inverse problems were first encountered in practice and are mostly ill-posed. The urgent need for their solution, especially in geological exploration and medical diagnostics, has given powerful impetus to the development of the theory of ill-posed problems. Nowadays, the terms "inverse problem" and "ill-posed problem" are inextricably linked to each other. Inverse and ill-posed problems are currently attracting great interest. A vast literature is devoted to these problems, making it necessary to systematize the accumulated material. This book is the first small step in that direction. We propose a classification of inverse problems according to the type of equation, unknowns and additional information. We consider specific problems from a single position and indicate relationships between them. The problems relate to different areas of mathematics, such as linear algebra, theory of integral equations, integral geometry, spectral theory and mathematical physics. We give examples of applied problems that can be studied using the techniques we describe. This book was conceived as a textbook on the foundations of the theory of inverse and ill-posed problems for university students. The author's intention was to explain this complex material in the most accessible way possible. The monograph is aimed primarily at those who are just beginning to get to grips with inverse and ill-posed problems but we hope that it will be useful to anyone who is interested in the subject. 410 0$aInverse and ill-posed problems series ;$vv. 55. 606 $aInverse problems (Differential equations) 606 $aBoundary value problems$xImproperly posed problems 608 $aElectronic books. 615 0$aInverse problems (Differential equations) 615 0$aBoundary value problems$xImproperly posed problems. 676 $a515/.357 700 $aKabanikhin$b S. I$0725459 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910465261203321 996 $aInverse and ill-posed problems$92442784 997 $aUNINA