Inverse Problems and Carleman Estimates: Global Uniqueness, Global Convergence and Experimental Data
Inverse and ill-posed problems series ;, v. 63./ Michael V. Klibanov, Jingzhi Li.

Li Jingzhi; Klibanov M. V. ((Michael V.),)

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dc.contributor.author	Klibanov M. V. ((Michael V.),)
dc.contributor.author	Li Jingzhi
dc.date.accessioned	2024-01-26T21:44:10Z
dc.date.available	2024-01-26T21:44:10Z
dc.date.issued	2021
dc.identifier.citation	Klibanov M. V. Inverse Problems and Carleman Estimates: Global Uniqueness, Global Convergence and Experimental Data Inverse and ill-posed problems series ;, v. 63. - 1 online resource (XVI, 328 p.). - URL: https://libweb.kpfu.ru/ebsco/pdf/3063088.pdf
dc.identifier.isbn	3110745488
dc.identifier.isbn	9783110745481
dc.identifier.uri	https://dspace.kpfu.ru/xmlui/handle/net/178922
dc.description	In English.
dc.description.abstract	This book summarizes the main analytical and numerical results of Carleman estimates. In the analytical part, Carleman estimates for three main types of Partial Differential Equations (PDEs) are derived. In the numerical part, first numerical methods are proposed to solve ill-posed Cauchy problems for both linear and quasilinear PDEs. Next, various versions of the convexification method are developed for a number of Coefficient Inverse Problems.
dc.description.tableofcontents	Frontmatter -- Preface -- Acknowledgments -- Contents -- 1 Topics of this book -- 2 Carleman estimates and Hölder stability for ill-posed Cauchy problems -- 3 Global uniqueness for coefficient inverse problems and Lipschitz stability for a hyperbolic CIP -- 4 The quasi-reversibility numerical method for ill-posed Cauchy problems for linear PDEs -- 5 Convexification for ill-posed Cauchy problems for quasi-linear PDEs -- 6 A special orthonormal basis in L2(a, b) for the convexification for CIPs without the initial conditions--restricted Dirichlet-to-Neumann map -- 7 Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data -- 8 Convexification for a coefficient inverse problem for a hyperbolic equation with a single location of the point source -- 9 Convexification for an inverse parabolic problem -- 10 Experimental data and convexification for the recovery of the dielectric constants of buried targets using the Helmholtz equation -- 11 Travel time tomography with formally determined incomplete data in 3D -- 12 Numerical solution of the linearized travel time tomography problem with incomplete data -- Bibliography -- Index
dc.language	English
dc.language.iso	en
dc.relation.ispartofseries	Inverse and Ill-Posed Problems Series. volume 63
dc.relation.ispartofseries	Inverse and ill-posed problems series ;. v. 63.
dc.subject.other	Inverse problems (Differential equations)
dc.subject.other	Carleman theorem.
dc.subject.other	Identifikationsverfahren.
dc.subject.other	Inverses Problem.
dc.subject.other	Numerische Mathematik.
dc.subject.other	Electronic books.
dc.title	Inverse Problems and Carleman Estimates: Global Uniqueness, Global Convergence and Experimental Data Inverse and ill-posed problems series ;, v. 63./ Michael V. Klibanov, Jingzhi Li.
dc.type	Book
dc.description.pages	1 online resource (XVI, 328 p.).
dc.collection	Электронно-библиотечные системы
dc.source.id	EN05CEBSCO05C2818