Описание: This book presents a unifiedapproach to studying the stability of both elliptic Cauchy problems and selectedinverse problems. Based on elementary Carleman inequalities, it establishesthree-ball inequalities, which are the key to deriving logarithmic stabilityestimates for elliptic Cauchy problems and are also useful in proving stabilityestimates for certain elliptic inverse problems. The book presents three inverseproblems, the first of which consists in determining the surface impedance ofan obstacle from the far field pattern. The second problem investigates the detectionof corrosion by electric measurement, while the third concerns thedetermination of an attenuation coefficient from internal data, which ismotivated by a problem encountered in biomedical imaging.
Описание: Consists of 14 research articles that are an outgrowth of a scientific meeting held in Cortona on the subject of Carleman Estimates and Control Theory. This volume includes topics such as unique continuation for elliptic PDEs and systems, control theory and inverse problems. It is suitable for researchers and graduate students of pdes.
Описание: The articles in this volume reflect a subsequent development after a scientific meeting entitled Carleman Estimates and Control Theory, held in Cartona in September 1999. The 14 research-level articles, written by experts, focus on new results on Carleman estimates and their applications to uniqueness and controlla- bility of partial differential equations and systems. The main topics are unique continuation for elliptic PDEs and systems, con- trol theory and inverse problems. New results on strong uniqueness for second or higher order operators are explored in detail in several papers. In the area of control theory. the reader will find applications of Carleman estimates to stabiliza- tion, observability and exact control for the wave and the SchrOdinger equations. A final paper presents a challenging list of open problems on the topic of control- lability of linear and sernilinear heat equations. The papers contain exhaustive and essentially self-contained proofs directly ac- cessible to mathematicians, physicists, and graduate students with an elementary background in PDEs. Contributors are L. Aloui, M. Bellassoued, N. Burq, F. Colombini, B. Dehman, C. Grammatico, M. Khenissi, H. Koch, P. Le Borgne, N. Lerner, T. Nishitani. T. Okaji, K.D. Phung, R. Regbaoui, X. Saint Raymond, D. Tataru, and E. Zuazua.
Описание: 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 non-overdetermining data of solutions.
Описание: 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 non-overdetermining data of solutions.
Автор: Klibanov Li Michael V. Jingzhi Название: Inverse Problems and Carleman Estimates ISBN: 3110745410 ISBN-13(EAN): 9783110745412 Издательство: Walter de Gruyter Рейтинг: Цена: 54601.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
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.
Описание: Acorrigendum and improvements to Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations and its Consequences.
Автор: Qin Yuming Название: Global Existence and Uniqueness of Nonlinear Evolutionary Fl ISBN: 3034805934 ISBN-13(EAN): 9783034805933 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Here are recent results in nonlinear evolutionary fluid equations such as compressible magnetohydrodynamics equations, compressible viscous micropolar fluid equations, full non-Newtonian fluid equations and non-autonomous compressible Navier-Stokes equations.
Описание: This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation.
Описание: Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. This book offers an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. It can be used as an introductory text to the theory underpinning fitted mesh methods.
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