Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations, T. Alazard, N. Burq, C. Zuily
Автор: Ti-Jun Xiao; Jin Liang Название: The Cauchy Problem for Higher Order Abstract Differential Equations ISBN: 3540652388 ISBN-13(EAN): 9783540652380 Издательство: Springer Рейтинг: Цена: 46540.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Useful for scientists and engineers in differential equations, analysis and functional analysis, mathematical physics, control theory, mechanics and engineering, and for graduate students in these disciplines.
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: 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: Melnikova, Irina V. , Filinkov, Alexei Название: Abstract Cauchy Problems ISBN: 0367397471 ISBN-13(EAN): 9780367397470 Издательство: Taylor&Francis Рейтинг: Цена: 65320.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularization methods. Semigroup and distribution methods restore well-posedness, in a modern weak sense. Regularization methods provide approximate solutions to ill-posed problems. Although these approaches were extensively developed over the last decades by many researchers, nowhere could one find a comprehensive treatment of all three approaches.
Abstract Cauchy Problems: Three Approaches provides an innovative, self-contained account of these methods and, furthermore, demonstrates and studies some of the profound connections between them. The authors discuss the application of different methods not only to the Cauchy problem that is not well-posed in the classical sense, but also to important generalizations: the Cauchy problem for inclusion and the Cauchy problem for second order equations. Accessible to nonspecialists and beginning graduate students, this volume brings together many different ideas to serve as a reference on modern methods for abstract linear evolution equations.
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.
