Carleman Estimates for Second Order Partial Differential Operators and Applications, Xiaoyu Fu; Qi L?; Xu Zhang

Автор: Lopez Gomez Julian
Название: Linear Second Order Elliptic Operators
ISBN: 9814440248 ISBN-13(EAN): 9789814440240
Издательство: World Scientific Publishing
Цена: 48570.00 T
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Описание: The main goal of the book is to provide a comprehensive and self-contained proof of the, relatively recent, theorem of characterization of the strong maximum principle due to Molina-Meyer and the author, published in Diff. Int. Eqns. in 1994, which was later refined by Amann and the author in a paper published in J. of Diff. Eqns. in 1998. Besides this characterization has been shown to be a pivotal result for the development of the modern theory of spatially heterogeneous nonlinear elliptic and parabolic problems; it has allowed us to update the classical theory on the maximum and minimum principles by providing with some extremely sharp refinements of the classical results of Hopf and Protter-Weinberger. By a celebrated result of Berestycki, Nirenberg and Varadhan, Comm. Pure Appl. Maths. in 1994, the characterization theorem is partially true under no regularity constraints on the support domain for Dirichlet boundary conditions.Instead of encyclopedic generality, this book pays special attention to completeness, clarity and transparency of its exposition so that it can be taught even at an advanced undergraduate level. Adopting this perspective, it is a textbook; however, it is simultaneously a research monograph about the maximum principle, as it brings together for the first time in the form of a book, the most paradigmatic classical results together with a series of recent fundamental results scattered in a number of independent papers by the author of this book and his collaborators.Chapters 3, 4, and 5 can be delivered as a classical undergraduate, or graduate, course in Hilbert space techniques for linear second order elliptic operators, and Chaps. 1 and 2 complete the classical results on the minimum principle covered by the paradigmatic textbook of Protter and Weinberger by incorporating some recent classification theorems of supersolutions by Walter, 1989, and the author, 2003. Consequently, these five chapters can be taught at an undergraduate, or graduate, level. Chapters 6 and 7 study the celebrated theorem of Krein-Rutman and infer from it the characterizations of the strong maximum principle of Molina-Meyer and Amann, in collaboration with the author, which have been incorporated to a textbook by the first time here, as well as the results of Chaps. 8 and 9, polishing some recent joint work of Cano-Casanova with the author. Consequently, the second half of the book consists of a more specialized monograph on the maximum principle and the underlying principal eigenvalues.

Автор: P. Cannarsa, P. Martinez, J. Vancostenoble
Название: Global Carleman Estimates for Degenerate Parabolic Operators with Applications
ISBN: 1470414961 ISBN-13(EAN): 9781470414962
Издательство: Mare Nostrum (Eurospan)
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Цена: 99790.00 T
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Описание: Introduces the reader to global Carleman estimates for a class of parabolic operators which may degenerate at the boundary of the space domain, in the normal direction to the boundary. Such a kind of degeneracy is relevant to study the invariance of a domain with respect to a given stochastic diffusion flow, and appears naturally in climatology models.

Автор: Feruccio Colombini; Claude Zuily
Название: Carleman Estimates and Applications to Uniqueness and Control Theory
ISBN: 1461266602 ISBN-13(EAN): 9781461266600
Издательство: Springer
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Цена: 93160.00 T
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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.

Автор: Mourad Bellassoued; Masahiro Yamamoto
Название: Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems
ISBN: 4431565981 ISBN-13(EAN): 9784431565987
Издательство: Springer
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Цена: 88500.00 T
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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: Genni Fragnelli, Dimitri Mugnai
Название: Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations
ISBN: 1470419548 ISBN-13(EAN): 9781470419547
Издательство: Mare Nostrum (Eurospan)
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Цена: 72990.00 T
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Описание: The authors consider a parabolic problem with degeneracy in the interior of the spatial domain, and they focus on observability results through Carleman estimates for the associated adjoint problem. The novelties of the present paper are two. First, the coefficient of the leading operator only belongs to a Sobolev space. Second, the degeneracy point is allowed to lie even in the interior of the control region, so that no previous result can be adapted to this situation; however, different cases can be handled, and new controllability results are established as a consequence.

Автор: Feruccio Colombini; Claude Zuily
Название: Carleman Estimates and Applications to Uniqueness and Control Theory
ISBN: 0817642307 ISBN-13(EAN): 9780817642303
Издательство: Springer
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Цена: 111790.00 T
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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.

Автор: Choulli
Название: Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems
ISBN: 331933641X ISBN-13(EAN): 9783319336411
Издательство: Springer
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Цена: 46570.00 T
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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.

Автор: Nicolas Lerner
Название: Carleman Inequalities
ISBN: 3030159922 ISBN-13(EAN): 9783030159924
Издательство: Springer
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Цена: 111790.00 T
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Описание: Over the past 25 years, Carleman estimates have become an essential tool in several areas related to partial differential equations such as control theory, inverse problems, or fluid mechanics. This book provides a detailed exposition of the basic techniques of Carleman Inequalities, driven by applications to various questions of unique continuation.

Автор: Amnon Pazy
Название: Semigroups of Linear Operators and Applications to Partial Differential Equations
ISBN: 1461255635 ISBN-13(EAN): 9781461255635
Издательство: Springer
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Цена: 121110.00 T
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Описание: Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations.

Автор: Lopez Velazquez Gustavo
Название: Partial Differential Equations Of First Order And Their Applications To Physics (2Nd Edition)
ISBN: 9814390372 ISBN-13(EAN): 9789814390378
Издательство: World Scientific Publishing
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Цена: 60190.00 T
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Описание: Intends to point out the mathematical importance of the Partial Differential Equations of First Order (PDEFO) in Physics and Applied Sciences. This edition covers the applications of PDEFO in several branches of applied mathematics. It also includes corrected typographical errors, new applications in Chapters 1, 2, and 5, and expanded examples.

Автор: Karl K. Sabelfeld, Irina A. Shalimova
Название: Spherical and Plane Integral Operators for PDEs: Construction, Analysis, and Applications
ISBN: 3110315297 ISBN-13(EAN): 9783110315295
Издательство: Walter de Gruyter
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Цена: 185890.00 T
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Описание: The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.

Автор: Luigi Rodino; M. W. Wong; Hongmei Zhu
Название: Pseudo-Differential Operators: Analysis, Applications and Computations
ISBN: 3034803230 ISBN-13(EAN): 9783034803236
Издательство: Springer
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Цена: 93160.00 T
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Описание: Based on the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at Imperial College London, this volume provides pseudo-differential operators. Topics include the analysis, applications and computations of pseudo-differential operators in mathematics.