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Nonlinear PDEs: A Dynamical Systems Approach, Guido Schneider, Hannes Uecker


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Автор: Guido Schneider, Hannes Uecker
Название:  Nonlinear PDEs: A Dynamical Systems Approach
ISBN: 9781470436131
Издательство: Mare Nostrum (Eurospan)
Классификация:

ISBN-10: 1470436132
Обложка/Формат: Hardback
Страницы: 584
Вес: 1.15 кг.
Дата издания: 30.11.2017
Серия: Graduate studies in mathematics
Язык: English
Размер: 188 x 261 x 36
Читательская аудитория: Professional and scholarly
Ключевые слова: Differential calculus & equations
Подзаголовок: A dynamical systems approach
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Поставляется из: Англии
Описание: This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs.The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrodinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given.The parts of the book are kept as self-contained as possible. The book is suitable for self-study, and there are various possibilities to build one- or two-semester courses from the book.
Дополнительное описание: Differential calculus and equations


Advances in Superprocesses and Nonlinear PDEs

Автор: Janos Englander; Brian Rider
Название: Advances in Superprocesses and Nonlinear PDEs
ISBN: 1489973338 ISBN-13(EAN): 9781489973337
Издательство: Springer
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Цена: 102480.00 T
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Описание: Sergei Kuznetsov is one of the top experts on measure valued branching processes (also known as "superprocesses") and their connection to nonlinear partial differential operators. His research interests range from stochastic processes and partial differential equations to mathematical statistics, time series analysis and statistical software;

Advances in Superprocesses and Nonlinear PDEs

Автор: Englander Janos
Название: Advances in Superprocesses and Nonlinear PDEs
ISBN: 1461462398 ISBN-13(EAN): 9781461462392
Издательство: Springer
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Цена: 102480.00 T
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Описание: Sergei Kuznetsov is one of the top experts on measure valued branching processes (also known as "superprocesses") and their connection to nonlinear partial differential operators. His research interests range from stochastic processes and partial differential equations to mathematical statistics, time series analysis and statistical software;

Nonlinear PDEs

Автор: Marius Ghergu; Vicentiu RADULESCU
Название: Nonlinear PDEs
ISBN: 3642269842 ISBN-13(EAN): 9783642269844
Издательство: Springer
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Цена: 93160.00 T
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Описание: This book shows how to apply theoretical mathematical models to unravel the mechanisms involved in processes found in mathematical physics and the biosciences. It is a unique collection of abstract methods that deploy nonlinear partial differential equations.

Stochastic PDEs and Dynamics

Автор: Boling Guo, Hongjun Gao, Xueke Pu
Название: Stochastic PDEs and Dynamics
ISBN: 3110495104 ISBN-13(EAN): 9783110495102
Издательство: Walter de Gruyter
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Цена: 123910.00 T
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Описание: This book explains mathematical theories of a collection of stochastic partial differential equations and their dynamical behaviors. Based on probability and stochastic process, the authors discuss stochastic integrals, Ito formula and Ornstein-Uhlenbeck processes, and introduce theoretical framework for random attractors. With rigorous mathematical deduction, the book is an essential reference to mathematicians and physicists in nonlinear science. Contents: PreliminariesThe stochastic integral and It formulaOU processes and SDEsRandom attractorsApplicationsBibliographyIndex

Nonlinear Stochastic PDEs

Автор: Tadahisa Funaki; Wojbor Woyczynski
Название: Nonlinear Stochastic PDEs
ISBN: 1461384702 ISBN-13(EAN): 9781461384700
Издательство: Springer
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Цена: 111790.00 T
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Описание: This IMA Volume in Mathematics and its Applications NONLINEAR STOCHASTIC PDEs: HYDRODYNAMIC LIMIT AND BURGERS` TURBULENCE is based on the proceedings of the period of concentration on Stochas- tic Methods for Nonlinear PDEs which was an integral part of the 1993- 94 IMA program on "Emerging Applications of Probability."

Spherical and Plane Integral Operators for PDEs: Construction, Analysis, and Applications

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.

Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs

Автор: Elemer E. Rosinger
Название: Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs
ISBN: 0792352327 ISBN-13(EAN): 9780792352327
Издательство: Springer
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Цена: 88500.00 T
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Описание: Presents global actions of arbitrary Lie groups on large classes of generalised functions by using a novel parametric approach. This volume is addressed to graduate students involved in solving linear and nonlinear partial differential equations, and in particular, dealing with the Lie group symmetries of their classical or generalised solutions.

High Order Nonlinear Numerical Schemes for Evolutionary PDEs

Автор: R?mi Abgrall; H?lo?se Beaugendre; Pietro Marco Con
Название: High Order Nonlinear Numerical Schemes for Evolutionary PDEs
ISBN: 3319381725 ISBN-13(EAN): 9783319381725
Издательство: Springer
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Цена: 111790.00 T
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Описание: This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013.

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Автор: Morris W. Hirsch
Название: Differential Equations, Dynamical Systems, and an Introduction to Chaos
ISBN: 0123820103 ISBN-13(EAN): 9780123820105
Издательство: Elsevier Science
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Цена: 88690.00 T
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Описание: Suitable for students in the fields of mathematics, science, and engineering, this title provides a theoretical approach to dynamical systems and chaos. It helps them to analyze the types of differential equations that arise in their area of study.

Free Boundary Problems in PDEs and Particle Systems

Автор: Carinci
Название: Free Boundary Problems in PDEs and Particle Systems
ISBN: 3319333690 ISBN-13(EAN): 9783319333694
Издательство: Springer
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Цена: 46570.00 T
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Описание:

In this volume a theory for models of transport in the presence of a free boundary is developed.
Macroscopic laws of transport are described by PDE's.
When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interaction with the exterior takes place in correspondence of a free boundary is considered. Both continuous and discrete models sharing the same structure are analysed.
In Part I a free boundary problem related to the Stefan Problem is worked out in all details. For this model a new notion of relaxed solution is proposed for which global existence and uniqueness is proven. It is also shown that this is the hydrodynamic limit of the empirical mass density of the associated particle system. In Part II several other models are discussed. The expectation is that the results proved for the basic model extend to these other cases.
All the models discussed in this volume have an interest in problems arising in several research fields such as heat conduction, queuing theory, propagation of fire, interface dynamics, population dynamics, evolution of biological systems with selection mechanisms.
In general researchers interested in the relations between PDE’s and stochastic processes can find in this volume an extension of this correspondence to modern mathematical physics.

Fully Nonlinear PDEs in Real and Complex Geometry and Optics

Автор: Luca Capogna; Pengfei Guan; Cristian E. Guti?rrez;
Название: Fully Nonlinear PDEs in Real and Complex Geometry and Optics
ISBN: 3319009419 ISBN-13(EAN): 9783319009414
Издательство: Springer
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Цена: 32600.00 T
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Описание:

Introduction.- L∞ extremal mappings in AMLE and Teichmьller theory.- Curvature Measures, Isoperimetric Type Inequalities and Fully Nonlinear Pde's.- Refraction Problems In Geometric Optics.- On the Levi Monge-Ampиre equation.



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