LEADER 05458nam 22006735 450 001 9910254292803321 005 20200701093335.0 010 $a4-431-56600-7 024 7 $a10.1007/978-4-431-56600-7 035 $a(CKB)4340000000223617 035 $a(DE-He213)978-4-431-56600-7 035 $a(MiAaPQ)EBC5161596 035 $a(PPN)221249885 035 $a(EXLCZ)994340000000223617 100 $a20171124d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCarleman Estimates and Applications to Inverse Problems for Hyperbolic Systems /$fby Mourad Bellassoued, Masahiro Yamamoto 205 $a1st ed. 2017. 210 1$aTokyo :$cSpringer Japan :$cImprint: Springer,$d2017. 215 $a1 online resource (XII, 260 p. 7 illus., 2 illus. in color.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 311 $a4-431-56598-1 320 $aIncludes bibliographical references and index. 327 $a1. Basics of Carleman estimates -- 2. Basic tools of Riemannian geometry -- 3. Well-posedness and regularity of the wave equation with variable coefficients -- 4. Carleman estimate of the wave equation in a Riemannian manifold -- 5. Inverse problem and Exact controllability for the wave equation in a Riemannian manifold -- 6. Carleman estimates for some thermoelasticity systems -- 7. Inverse heat source problem for the thermoelasticity system with variable coefficients -- 8. New realization of the pseudoconvexity -- 9. Stability in an inverse problem for a hyperbolic equation with a finite set of boundary data -- 10. Global Carleman estimate for the Laplace-Beltrami operator with an extra elliptic variable and applications. 330 $aThis book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions. The formulation is different from that of Dirichlet-to-Neumann maps and can often prove the global uniqueness and Lipschitz stability even with a single measurement. These types of inverse problems include coefficient inverse problems of determining physical parameters in inhomogeneous media that appear in many applications related to electromagnetism, elasticity, and related phenomena. Although the methodology was created in 1981 by Bukhgeim and Klibanov, its comprehensive development has been accomplished only recently. In spite of the wide applicability of the method, there are few monographs focusing on combined accounts of Carleman estimates and applications to inverse problems. The aim in this book is to fill that gap. The basic tool is Carleman estimates, the theory of which has been established within a very general framework, so that the method using Carleman estimates for inverse problems is misunderstood as being very difficult. The main purpose of the book is to provide an accessible approach to the methodology. To accomplish that goal, the authors include a direct derivation of Carleman estimates, the derivation being based essentially on elementary calculus working flexibly for various equations. Because the inverse problem depends heavily on respective equations, too general and abstract an approach may not be balanced. Thus a direct and concrete means was chosen not only because it is friendly to readers but also is much more relevant. By practical necessity, there is surely a wide range of inverse problems and the method delineated here can solve them. The intention is for readers to learn that method and then apply it to solving new inverse problems. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aDifferential equations, Partial 606 $aFunctional analysis 606 $aGeometry, Differential 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aMathematical physics 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 615 0$aDifferential equations, Partial. 615 0$aFunctional analysis. 615 0$aGeometry, Differential. 615 0$aManifolds (Mathematics) 615 0$aComplex manifolds. 615 0$aMathematical physics. 615 14$aPartial Differential Equations. 615 24$aFunctional Analysis. 615 24$aDifferential Geometry. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 615 24$aMathematical Physics. 676 $a515.353 700 $aBellassoued$b Mourad$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767514 702 $aYamamoto$b Masahiro$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910254292803321 996 $aCarleman Estimates and Applications to Inverse Problems for Hyperbolic Systems$92179911 997 $aUNINA