Asymptotic Perturbation Methods: For Nonlinear Differential Equations in Physics, Attilio Maccari
Автор: Holmes Mark H Название: Introduction to Perturbation Methods ISBN: 146145476X ISBN-13(EAN): 9781461454762 Издательство: Springer Рейтинг: Цена: 39130.00 T Наличие на складе: Есть Описание: Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.One hundred new pages added including new material on transcedentally small terms, Kummer`s function, weakly coupled oscillators and wave interactions.
Автор: Johannes Sj?strand Название: Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations ISBN: 303010818X ISBN-13(EAN): 9783030108182 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago.In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book.Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
Автор: Fumio Hiroshima Название: Ground States of Quantum Field Models ISBN: 9813293047 ISBN-13(EAN): 9789813293045 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This book provides self-contained proofs of the existence of ground states of several interaction models in quantum field theory. Interaction models discussed here include the spin-boson model, the Nelson model with and without an ultraviolet cutoff, and the Pauli–Fierz model with and without dipole approximation in non-relativistic quantum electrodynamics. These models describe interactions between bose fields and quantum mechanical matters.
A ground state is defined as the eigenvector associated with the bottom of the spectrum of a self-adjoint operator describing the Hamiltonian of a model. The bottom of the spectrum is however embedded in the continuum and then it is non-trivial to show the existence of ground states in non-perturbative ways. We show the existence of the ground state of the Pauli–Fierz mode, the Nelson model, and the spin-boson model, and several kinds of proofs of the existence of ground states are explicitly provided. Key ingredients are compact sets and compact operators in Hilbert spaces. For the Nelson model with an ultraviolet cutoff and the Pauli–Fierz model with dipole approximation we show not only the existence of ground states but also enhanced binding. The enhanced binding means that a system for zero-coupling has no ground state but it has a ground state after turning on an interaction.
The book will be of interest to graduate students of mathematics as well as to students of the natural sciences who want to learn quantum field theory from a mathematical point of view. It begins with abstract compactness arguments in Hilbert spaces and definitions of fundamental facts of quantum field theory: boson Fock spaces, creation operators, annihilation operators, and second quantization. This book quickly takes the reader to a level where a wider-than-usual range of quantum field theory can be appreciated, and self-contained proofs of the existence of ground states and enhanced binding are presented.
Автор: Mi-Ho Giga; Yoshikazu Giga; J?rgen Saal Название: Nonlinear Partial Differential Equations ISBN: 0817641734 ISBN-13(EAN): 9780817641733 Издательство: Springer Рейтинг: Цена: 74530.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Focuses on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This book features exercises, examples, and illustrations to help explain the rigorous analytic basis for the Navier-Stokes equations, and mean curvature flow equations.
Автор: J.S. Joel; V.M. Babich; M.V. Fedoryuk; N.S. Bakhva Название: Partial Differential Equations V ISBN: 3540533710 ISBN-13(EAN): 9783540533719 Издательство: Springer Рейтинг: Цена: 136910.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The six articles in this EMS volume provide an overview of a number of mid-to-late-1990s techniques in the study of the asymptotic behaviour of partial differential equations. These techniques include the Maslov canonical operator, and semiclassical asymptotics of solutions and eigenfunctions.
Автор: Marchuk, Guri I. , Agoshkov, Valeri I. , Shutyae Название: Adjoint Equations and Perturbation Algorithms in Nonlinear Problems ISBN: 0367448580 ISBN-13(EAN): 9780367448585 Издательство: Taylor&Francis Рейтинг: Цена: 67360.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book presents the theory of adjoint equations in nonlinear problems and their applications to perturbation algorithms for solution of nonlinear problems in mathematical physics. It formulates a series of principles of construction of adjoint operators in nonlinear problems.
Автор: V.N. Bogaevski; A. Povzner Название: Algebraic Methods in Nonlinear Perturbation Theory ISBN: 1461287707 ISBN-13(EAN): 9781461287704 Издательство: Springer Рейтинг: Цена: 104480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Of interest to everybody working on perturbation theory in differential equations, this book requires only a standard mathematical background in engineering and does not require reference to the special literature. systems of ordinary differential equations with small parameters; reconstruction and equations in partial derivatives.
Автор: Valery V. Kozlov; Stanislav D. Furta; Lester Senec Название: Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations ISBN: 3642432409 ISBN-13(EAN): 9783642432408 Издательство: Springer Рейтинг: Цена: 111790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: With a pedagogic format ideal for graduate students, this text includes a wealth of examples focusing on solutions in dynamical systems theory that mirror those used in Lyapunov`s first method, tackling ordinary differential equations expressed as series form.
Автор: Jacqueline Sanchez Hubert Название: Vibration and Coupling of Continuous Systems ISBN: 3642737846 ISBN-13(EAN): 9783642737848 Издательство: Springer Рейтинг: Цена: 95770.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Real problems concerning vibrations of elastic structures are among the most fascinating topics in mathematical and physical research as well as in applications in the engineering sciences.
Автор: H.G. Kaper; Gail W. Pieper; Marc Garbey Название: Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters ISBN: 0792320611 ISBN-13(EAN): 9780792320616 Издательство: Springer Рейтинг: Цена: 277650.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: A record of the workshop on asymptotic-induced numerical methods for partial differential equations, critical parameters and domain decomposition, held at Beaune, France. The book discusses new computational methods, recent algorithm developments and techniques in mathematical modelling.
Автор: Ostrovsky Lev Название: Asymptotic Perturbation Theory Of Waves ISBN: 1848162359 ISBN-13(EAN): 9781848162358 Издательство: World Scientific Publishing Рейтинг: Цена: 87650.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Presents an introduction to the perturbation theory for nonlinear waves in dispersive and dissipative media. This work generalizes the integrable evolution equations to include effects of dissipation, inhomogeneity and media rotation. It also considers non-integrable model equations.
Автор: Bender, Carl M. (washington University, Usa) Orsza Название: Advanced mathematical methods for scientists and engineers ISBN: 0387989315 ISBN-13(EAN): 9780387989310 Издательство: Springer Рейтинг: Цена: 79190.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations.
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