2 edition of Carleman Estimates For Coefficient Inverse Problems And Numerical Applications (Inverse and Ill-Posed Problems Series) found in the catalog.
by Brill Academic Publishers
Written in English
|The Physical Object|
|Number of Pages||280|
Inverse coefficient problems for a transport equation by local Carleman estimate. P Cannarsa 1, G Floridia 2, F Gölgeleyen 3 and M Yamamoto 4,5,6. Klibanov M V and Timonov A Carleman Estimates for Coefficient Inverse Problems and Numerical Applications (Utrecht: VSP) Crossref Google ScholarCited by: 7. The Lipschitz stability estimate for a coefficient inverse problem for the non-stationary single-speed transport equation with the lateral boundary data is obtained. The method of Carleman estimates is used. Uniqueness of the solution follows. 1. Introduction The transport equation is used to model a variety of diffusion processes, such as.
Therefore it is very desirable that such conditions should be directly checked. Otherwise an admissible set to which unknown coefficients can be assumed to belong is too special and narrow. Thus our Carleman estimate is more feasible for the application to inverse problems. Next we apply Theorem 1 to the unique continuation and an inverse by: Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems $ DOWNLOAD THIS EBOOK. Delivery: Can be download Immediately after new customer, we need process for verification from 30 mins to 24 hours.
Get this from a library! Carleman estimates and applications to inverse problems for hyperbolic systems. [Mourad Bellassoued; Masahiro Yamamoto] -- This 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. M.V. Klibanov, A. Timonov, Carleman Estimates for Coeï¬ƒcient Inverse Problems and Numerical Applications, Inverse and Ill-posed Problems Series, VSP, Utrecht, , iv+ pp.  P. Martinez, J. Vancostenoble, Carleman estimates for one-dimensional degenerate heat equations, J. Evol. Equ. 6 (2) () â€“ Cited by: 7.
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Series: INVERSE AND ILL-POSED PROBLEMS SERIES (Book 46) Hardcover: pages; Publisher: De Gruyter (Ma ) Language: English; ISBN ; ISBN ; Product Dimensions: 6 x x 9 inches Shipping Weight: pounds; Customer Reviews: Be the first to write a reviewAuthor: Michael V.
Klibanov, Alexander A. Timonov. 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. Buy Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems (Springer Monographs in Mathematics) on FREE SHIPPING on qualified ordersCited by: As to coefficient inverse problems, the idea of applications of Carleman estimates to proofs of uniqueness and stability theorems for them were originally proposed in the paper of Bukhgeim and.
In this monograph, the main subject of the author's considerations is coefficient inverse problems. Arising in many areas of natural sciences and technology, such problems consist of determining the variable coefficients of a certain differential operator defined in a domain from boundary measurements of a solution or its functionals.
Chapter 2. Carleman estimates and ill-posed Cauchy problems; Chapter 3. Global uniqueness results in high dimensions; Chapter 4.
The global uniqueness of a nonlinear parabolic problem; Chapter 5. On the numerical solution of coefficient inverse problems; Chapter 6.
Some globally convergent convexification algorithms; Chapter 7. Some applied. a nonlinear parabolic problem Problem formulation Statement of the main result An estimate of an integral The integro-differential inequality Domains Notations A Carleman estimate Proof of the main result Chapter 5.
On the numerical solution of coefficient inverse. Carleman Estimates For Globally Convergent Numerical Methods for Coefficient Inverse Problems there is a fundamental challenge in the goal of the numerical solution of any CIP. Indeed, any CIP is both nonlinear and ill-posed. This is the function which is involved in the so-called Carleman estimate for the original PDE operator.
The authors prove Carleman estimates for the Schrödinger equation in Sobolev spaces of negative orders, and use these estimates to prove the uniqueness in the inverse problem of determining L p.
Carleman Estimates for Coefficient Inverse Problems and Numerical Applications Series: Inverse and Ill-Posed Problems Series 46 ,00 € / $ / £ *.
Inverse problems of determining coefficients and/or are not only theoretically challenging, but also important from the practical point of view. This inverse source problem is the essential first step towards the coefficient inverse problems because the inverse source problem can be regarded as a linearization of the coefficient inverse problem.
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. This book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems.
Based on elementary Carleman inequalities, it establishes three-ball ine. Carleman Estimates and Applications to Inverse Problems Article in Milan Journal of Mathematics 72(1) October with 20 Reads How we measure 'reads'Author: Victor Isakov.
Carleman estimate and an inverse source problem for the Kelvin-Voigt model for viscoelasticity Carleman Estimates for Coefficient Inverse Problems and Numerical Applications, VSP, Utrecht. In our method, the choice of the weight function in our Carleman estimate is essential for the application to inverse problems.
The weight function of our Carleman estimate (proposition 1 in section 2) is linear in t and similar to [ 7 ], but different from Cited by: 7.
In this paper, we consider Carleman-type estimates and an inverse source problem for second-order hyperbolic systems in an anisotropic case. In Part I, we establish a Carleman-type estimate for Author: Shumin Li.
The unknown spatially distributed speed of sound is the subject of the solution of this problem. A single location of the point source is used. Using a Carleman weight function, a globally strictly convex cost functional is constructed.
A new Carleman estimate is proven. Global convergence of the gradient projection method is proven. In this thesis, we study the inverse problem of the coupling phenomenon of electromagnetic (EM) and seismic waves. Partial differential equations governing the coupling phenomenon are composed of Maxwell and Biot equations.
Since the coupling phenomenon is rather weak, in low frequency we only consider the transformation from EM waves to seismic waves. We use electroseismic model to refer to Author: Qi Xue. ISBN: OCLC Number: Description: iv, pages: illustrations ; 25 cm. Contents: Ch. Introduction --Ch. an estimates and ill-posed Cauchy problems --Ch.
uniqueness results in high dimensions --Ch. global uniqueness of a nonlinear parabolic problem --Ch. the numerical solution of coefficient inverse problems --Ch.
Inverse coefficient problems for a transport equation by local Carleman estimate Piermarco Cannarsa, Giuseppe Floridia, Fikret Golgeleyen, Masahiro Yamamoto Mathematics.NUMERICAL METHODS FOR COEFFICIENT INVERSE PROBLEMS MICHAEL V.
KLIBANOV∗ Abstract. This is a review paper of the role of Carleman estimates in the theory of Multidimensional Coeﬃcient Inverse Problems since the ﬁrst inception of this idea in 1 Introduction 2 2 Carleman Estimates, Holder Stability and the Quasi-Reversibility Method 4.of an integral in the Carleman estimate, depending on the divergence term V, where the integration is carried out over t 0 (see Lemma 1).
In the case of hyperbolic inverse problems this integral is zero due to the Carleman estimate for the principal part of the hyperbolic operator, see Theorem in .