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010   $a3-031-86267-8
024 7 $a10.1007/978-3-031-86267-0
035   $a(CKB)40851819200041
035   $a(MiAaPQ)EBC32275494
035   $a(Au-PeEL)EBL32275494
035   $a(DE-He213)978-3-031-86267-0
035   $a(OCoLC)1535977109
035   $a(EXLCZ)9940851819200041
100   $a20250831d2025      u|         0
101 0 $aeng
135   $aur|||||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aIntroduction to Inverse Problems for Evolution Equations $eStability and Uniqueness by Carleman Estimates /$fby Masahiro Yamamoto
205   $a1st ed. 2025.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025.
215   $a1 online resource (412 pages)
225 1 $aLecture Notes of the Unione Matematica Italiana,$x1862-9121 ;$v29
311 08$a3-031-86266-X 
327   $a- 1. How inverse problems appear and what should we study about inverse problems? -- 2. Application of the multiplier method to an inverse wave source problem -- 3. Inverse problems by Carleman estimates for first-order transport equations -- 4. Inverse problems by Carleman estimates for parabolic equations -- 5. Inverse problems by Carleman estimates for hyperbolic equations -- 6. Conditional stability and convergence rates of the Tikhonov regularization -- 7. Other estimates of Carleman type -- 8. Derivation of Carleman estimates for elliptic equations.
330   $aAmong several main formulations, the book treats inverse problems with single measurements by Carleman estimates and describes a method for proving the uniqueness and the stability for the first-order transport equations, parabolic equations, and hyperbolic equations. The book gives self-contained derivations of Carleman estimates, which do not rely on any general theory and simplified application method of the Carleman estimates to the inverse problems. Thus, the target audience is graduate students of faculty of sciences and interested graduate students from engineering fields. The book tries to limit the preliminary knowledge to a standard 4-year undergraduate course. In order to master the methodology, we restrict equations within first-order transport equations, parabolic equations and hyperbolic equations, but it is expected to apply the same methods for other evolution equations such as fluid dynamics.
410  0$aLecture Notes of the Unione Matematica Italiana,$x1862-9121 ;$v29
606   $aMathematical analysis
606   $aMathematics
606   $aAnalysis
606   $aMathematics
615  0$aMathematical analysis.
615  0$aMathematics.
615 14$aAnalysis.
615 24$aMathematics.
676   $a515.357
700   $aYamamoto$b Masahiro$0767515
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9911022453603321
996   $aIntroduction to Inverse Problems for Evolution Equations$94431781
997   $aUNINA