The Cauchy Problem for Higher Order Abstract Differential Equations, Ti-Jun Xiao; Jin Liang
Автор: Strang Название: Differential Equations and Linear Algebra ISBN: 0980232791 ISBN-13(EAN): 9780980232790 Издательство: Cambridge Academ Рейтинг: Цена: 60180.00 T Наличие на складе: Невозможна поставка. Описание: Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.
Автор: Wolfgang Arendt; Charles J.K. Batty; Matthias Hieb Название: Vector-valued Laplace Transforms and Cauchy Problems ISBN: 3034803273 ISBN-13(EAN): 9783034803274 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In addition to systematic coverage of vector-valued Laplace transform theory, ranging from representation to Tauberian theorems, this second edition develops the theory of linear Cauchy problems and semigroups of operators and introduces the Bochner integral.
Автор: Choulli Название: Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems ISBN: 331933641X ISBN-13(EAN): 9783319336411 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. 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: Ingo Lieb; Joachim Michel Название: The Cauchy-Riemann Complex ISBN: 3322916103 ISBN-13(EAN): 9783322916105 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book presents complex analysis of several variables from the point of view of the Cauchy-Riemann equations and integral representations. A more detailed description of our methods and main results can be found in the introduction. Here we only make some remarks on our aims and on the required background knowledge. Integral representation methods serve a twofold purpose: 1 they yield regularity results not easily obtained by other methods and 2 , along the way, they lead to a fairly simple development of parts of the classical theory of several complex variables. We try to reach both aims. Thus, the first three to four chapters, if complemented by an elementary chapter on holomorphic functions, can be used by a lecturer as an introductory course to com- plex analysis. They contain standard applications of the Bochner-Martinelli-Koppelman integral representation, a complete presentation of Cauchy-Fantappie forms giving also the numerical constants of the theory, and a direct study of the Cauchy-Riemann com- plex on strictly pseudoconvex domains leading, among other things, to a rather elementary solution of Levi's problem in complex number space en. Chapter IV carries the theory from domains in en to strictly pseudoconvex subdomains of arbitrary - not necessarily Stein - manifolds. We develop this theory taking as a model classical Hodge theory on compact Riemannian manifolds; the relation between a parametrix for the real Laplacian and the generalised Bochner-Martinelli-Koppelman formula is crucial for the success of the method.
Автор: Xavier Tolsa Название: Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calder?n–Zygmund Theory ISBN: 3319345443 ISBN-13(EAN): 9783319345444 Издательство: Springer Рейтинг: Цена: 88500.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book studies some of the groundbreaking advances that have been made regarding analytic capacity and its relationship to rectifiability. It provides a unified approach to the material and simplified proofs.
Автор: Dragomir Название: Geometry of Cauchy-Riemann Submanifolds ISBN: 9811009155 ISBN-13(EAN): 9789811009150 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds.Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.
Автор: Tatsuo Nishitani Название: Cauchy Problem for Differential Operators with Double Characteristics ISBN: 3319676113 ISBN-13(EAN): 9783319676111 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well/ill-posed results related to the Cauchy problem for differential operators with non-effectively hyperbolic double characteristics. Previously scattered over numerous different publications, the results are presented from the viewpoint that the Hamilton map and the geometry of bicharacteristics completely characterizes the well/ill-posedness of the Cauchy problem. A doubly characteristic point of a differential operator P of order m (i.e. one where Pm = dPm = 0) is effectively hyperbolic if the Hamilton map FPm has real non-zero eigen values. When the characteristics are at most double and every double characteristic is effectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms. If there is a non-effectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between -Pj and Pj, where ij are the positive imaginary eigenvalues of FPm . Moreover, if 0 is an eigenvalue of FPm with corresponding 4 4 Jordan block, the spectral structure of FPm is insufficient to determine whether the Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly characteristic manifold plays a crucial role.
Автор: Xie Название: Differential Equations for Engineers ISBN: 1107632951 ISBN-13(EAN): 9781107632950 Издательство: Cambridge Academ Рейтинг: Цена: 63360.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Xie presents a systematic introduction to differential equations for engineering students. The relevance of differential equations in engineering applications motivates readers, and studies of various types of differential equations are determined by engineering applications. The theory and techniques for solving differential equations are then applied to solve practical engineering problems.
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