Описание: Partial differential equations are one of the most used widely forms of mathematics in science and engineering. Two fractional PDEs can be considered, fractional in time, and fractional in space. This volume is directed to the development and use of SFPDEs, providing a discussion of applications from classical integer PDEs.
Описание: Partial differential equations are one of the most used widely forms of mathematics in science and engineering. Two fractional PDEs can be considered, fractional in time, and fractional in space. These two volumes are directed to the development and use of SFPDEs, with the discussion divided into an introduction to Algorithms and Computer Coding in R and applications from classical integer PDEs.
Автор: Marcelo R. Ebert; Michael Reissig Название: Methods for Partial Differential Equations ISBN: 3319664557 ISBN-13(EAN): 9783319664552 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area.The book is organized in five parts:In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation.Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool for the treatment of non-stationary or evolution models and shows how to define energies for different models.Part 3 demonstrates how phase space analysis and interpolation techniques are used to prove decay estimates for solutions on and away from the conjugate line. It also examines how terms of lower order (mass or dissipation) or additional regularity of the data may influence expected results.Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the range of admissible powers in classes which make it possible to prove quite different qualitative properties of solutions, for example, the stability of the zero solution or blow-up behavior of local (in time) solutions. The last part features selected research projects and general background material.
Автор: Peter J. Olver Название: Introduction to Partial Differential Equations ISBN: 3319347446 ISBN-13(EAN): 9783319347448 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: ГЇВїВЅ ГЇВїВЅ This textbook is designed for a one year course covering the fundamentals of partial differential equations, aimed towards advanced undergraduates and beginning graduate students. It features examples and exercises connected to real world problems.
Автор: Zhang Xiang Название: Integrability of Dynamical Systems: Algebra and Analysis ISBN: 9811350825 ISBN-13(EAN): 9789811350825 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is the first book to systematically state the fundamental theory of integrability and its development of ordinary differential equations with emphasis on the Darboux theory of integrability and local integrability together with their applications.
Автор: Boris Kruglikov; Valentin Lychagin; Eldar Straume Название: Differential Equations - Geometry, Symmetries and Integrability ISBN: 3642269338 ISBN-13(EAN): 9783642269332 Издательство: Springer Рейтинг: Цена: 23058.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book contains papers presented at the Abel Symposium 2008, which focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. It presents a modern approach to this classical subject.
Описание: This book serves as an introduction to the concept of integrability as it applies to systems of differential equations as well as to vector-valued fields. The author focuses on specific aspects of integrability that are often encountered in a variety of problems in applied mathematics, physics and engineering. The following general cases of integrability are examined: (a) path-independence of line integrals of vector fields on the plane and in space; (b) integration of a system of ordinary differential equations by using first integrals; and (c) integrable systems of partial differential equations. Special topics include the integration of analytic functions and some elements from the geometric theory of differential systems. Certain more advanced subjects, such as Lax pairs and B?cklund transformations, are also discussed.The book is written at an intermediate level for educational purposes. The presentation is as simple as the topics allow, often sacrificing mathematical rigor in favor of pedagogical efficiency.
Описание: This book is devoted to the relation between two different concepts of integrability: the complete integrability of complex analytical Hamiltonian systems and the integrability of complex analytical linear differential equations.
Описание: This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations.
Описание: This is the first book devoted to the task of computing integrability structures by computer. The symbolic computation of integrability operator is a computationally hard problem and the book covers a huge number of situations through tutorials.
Автор: Boris Kruglikov; Valentin Lychagin; Eldar Straume Название: Differential Equations - Geometry, Symmetries and Integrability ISBN: 3642008720 ISBN-13(EAN): 9783642008726 Издательство: Springer Рейтинг: Цена: 23058.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. This title consists of original contributions and overview lectures of the participants of the Symposium. It includes papers that present the modern approach to this classical subject.
Описание: This book is devoted to the relation between two different concepts of integrability: the complete integrability of complex analytical Hamiltonian systems and the integrability of complex analytical linear differential equations.
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