Описание: The present volume is self-contained and introduces to the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis. Only some examples require more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Particular stress is on equations of the hyperbolic type since considerably less often treated in the literature. Also, evolution equations from fundamental physics need to be compatible with the theory of special relativity and therefore are of hyperbolic type. Throughout, detailed applications are given to hyperbolic partial differential equations occurring in problems of current theoretical physics, in particular to Hermitian hyperbolic systems. This volume is thus also of interest to readers from theoretical physics.
Описание: Numerical Solution of Hyperbolic Partial Differential Equations is a new type of graduate textbook, with both print and interactive electronic components (on CD). It is a comprehensive presentation of modern shock-capturing methods, including both finite volume and finite element methods, covering the theory of hyperbolic conservation laws and the theory of the numerical methods. The range of applications is broad enough to engage most engineering disciplines and many areas of applied mathematics. Classical techniques for judging the qualitative performance of the schemes are used to motivate the development of classical higher-order methods. The interactive CD gives access to the computer code used to create all of the text's figures, and lets readers run simulations, choosing their own input parameters; the CD displays the results of the experiments as movies. Consequently, students can gain an appreciation for both the dynamics of the problem application, and the growth of numerical errors.
Описание: In this introductory textbook, a revised and extended version of well-known lectures by L. Hormander from 1986, four chapters are devoted to weak solutions
of systems of conservation laws. Apart from that the book only studies classical solutions.
Two chapters concern the existence of global solutions or estimates of the lifespan
for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This
part assumes some familiarity with pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of opertors
needed in the nonlinear theory is presented in complete detail.
Автор: Alinhac, Serge Название: Hyperbolic partial differential equations ISBN: 038787822X ISBN-13(EAN): 9780387878225 Издательство: Springer Рейтинг: Цена: 5142 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. It includes more than 100 exercises, along with "do-it-yourself" instructions for the proofs of many theorems.
Автор: Ratcliffe Название: Foundations of Hyperbolic Manifolds ISBN: 0387331972 ISBN-13(EAN): 9780387331973 Издательство: Springer Рейтинг: Цена: 5138 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. This book has been heavily class-tested and each chapter contains exercises and a section of historical remarks.
Автор: Lang Название: Introduction to Complex Hyperbolic Spaces ISBN: 0387964479 ISBN-13(EAN): 9780387964478 Издательство: Springer Рейтинг: Цена: 12154 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Vojta has made quantitative conjectures by relating the Second Main Theorem of Nevan- linna theory to the theory of heights, and he has conjectured bounds on heights stemming from inequalities having to do with diophantine approximations and implying both classical and modern conjectures.
Описание: In the recent half-century, many mathematicians have investigated various problems on several equations of mixed type and obtained interesting results, with
important applications to gas dynamics. However, the Tricomi problem of general mixed type equations of second order with parabolic degeneracy has not been completely solved,
particularly the Tricomi and Frankl problems for general Chaplygin equation in multiply connected domains posed by L Bers, and the existence, regularity of solutions of the above
problems for mixed equations with non-smooth degenerate curve in several domains posed by J M Rassias.The method revealed in this book is unlike any other, in which the hyperbolic
number and hyperbolic complex function in hyperbolic domains, and the complex number and complex function in elliptic domains are used. The corresponding problems for first order
complex equations with singular coefficients are first discussed, and then the problems for second order complex equations are considered, where we pose the new partial derivative
notations and complex analytic methods such that the forms of the above first order complex equations in hyperbolic and elliptic domains are wholly identical.
In the meantime,
the estimates of solutions for the above problems are obtained, hence many open problems including the above Tricomi- Bers and Tricomi-Frankl-Rassias problems can be solved.
Описание: Consists of the proceedings of the 14th MSJ International Research Institute `Asymptotic Analysis and Singularity`, which was held at Sendai, Japan in July 2005. This title contains survey papers and original research papers on nonlinear partial differential equations, dynamical systems, calculus of variations and mathematical physics.
Описание: Uses the method of maximum likelihood to a large extent to ensure reasonable, and in some cases optimal procedures. This work treats the basic and important topics in multivariate statistics.
Автор: Anderson Название: Hyperbolic Geometry ISBN: 1852339349 ISBN-13(EAN): 9781852339340 Издательство: Springer Рейтинг: Цена: 3268 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The geometry of the hyperbolic plane is an active and fascinating field of mathematical inquiry. This book provides an introduction to the subject. Topics covered include the upper half-space model of the hyperbolic plane, Mobius transformations, arc-length and distance, the Poincare disc model, convex subsets of the hyperbolic plane, and more.
Описание: This book introduces geometric spectral theory in the context of Riemann surfaces. A comprehensive account is given of dramatic recent developments in the context of infinite-area hyperbolic surfaces. These developments were prompted by advances in geometric scattering theory in the early 1990s which provided new tools for the study of resonances. Hyperbolic surfaces provide an ideal context in which to introduce these developments, with technical difficulties kept to a minimum.Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, characterization of the spectrum, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson- Sullivan theory, and the dynamical approach to the zeta function.
Автор: Benedetti Riccardo, Petronio Carlo Название: Lectures on Hyperbolic Geometry ISBN: 354055534X ISBN-13(EAN): 9783540555346 Издательство: Springer Рейтинг: Цена: 3735 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The core of the book is the study of the space of the hyperbolic manifolds endowed with the Chabauty and the geometric topology, and in particular the proof of the hypberbolic surgery theorem in dimension three, based on the representation of three-mainfolds as glued ideal tetrahedra. The development of this main theme requires setting a wide background forming the body of the book: the classical geometry of the hyperbolic space, the Fenchel-Nielsen parametrization of the TeichmГјller space, Mostow's rigidity theorem, Margulis' lemma. As a conclusion some features of bounded cohomology, flat fiber bundles and amenable groups are mentioned.
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