Handbook of Differential Equations: Evolutionary Equations PDF Download

Author: C.M. Dafermos
Publisher: Elsevier
ISBN: 9780080461380
Category : Mathematics
Languages : en
Pages : 676

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Book Description
The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today. . Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.

Author: M. Chipot
Publisher:
ISBN: 9780444517432
Category : Differential equations
Languages : en
Pages : 616

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Book Description
This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Key features: - Written by well-known experts in the field - Self-contained volume in series covering one of the most rapid developing topics in mathematics - Written by well-known experts in the field - Self-contained volume in series covering one of the most rapid developing topics in mathematics.

Author: C.M. Dafermos
Publisher: Elsevier
ISBN: 0080931979
Category : Mathematics
Languages : en
Pages : 609

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Book Description
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts. - Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts

Author: Michel Chipot
Publisher:
ISBN: 9781280638497
Category : Differential equations
Languages : en
Pages : 0

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Book Description
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts. - Review of new results in the area - Continuation of previous volumes in the handbook series covering evolutionary PDEs - New content coverage of DE applications.

Author: Constantine M. Dafermos
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages :

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Book Description
This book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations. The main objective is to present clear, rigorous, and in depth surveys on the most important aspects of the present theory. The table of contents includes: W. Arendt: Semigroups and evolution equations: Calculus, regularity and kernel estimates A. Bressan: The front tracking method for systems of conservation laws E. DiBenedetto, J.M. Urbano, V. Vespri: Current issues on singular and degenerate evolution equations; L. Hsiao, S. Jiang: Nonlinear hyperbolic-parabolic coupled systems A. Lunardi: Nonlinear parabolic equations and systems D. Serre:L1-stability of nonlinear waves in scalar conservation laws B. Perthame:Kinetic formulations of parabolic and hyperbolic PDEs: from theory to numerics.

Author: Andrei D. Polyanin
Publisher: CRC Press
ISBN: 1135440816
Category : Mathematics
Languages : en
Pages : 835

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Book Description
The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:

Author: Xander Cooper
Publisher: Larsen and Keller Education
ISBN:
Category : Mathematics
Languages : en
Pages : 0

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Book Description
A differential equation is an equation, which contains at least one (ordinary or partial) derivative of an unknown function. There are different types of differential equations including ordinary differential equations, linear differential equations, partial differential equations, homogeneous differential equations, non-linear differential equations, and non-homogeneous differential equations. Differential equations can also be classified based on the order or coefficients of the derivatives, which may be either constants, or functions of the independent variable. These equations have several applications in fields such as physics, engineering, biology and applied mathematics. An evolution equation refers to a partial differential equation that describes the evolution of a physical system starting from a given initial data with respect to time. Researchers come across a variety of mathematical models that involve the use of evolutionary differential equations, both partial and ordinary, in multiple applications such as mathematical finance, fluid flow, image processing and computer vision, mechanical systems, relativity, physics-based animation, and Earth sciences. This book presents the complex subject of evolutionary differential equations in the most comprehensible and easy to understand language. It attempts to assist those with a goal of delving into the field of mathematics.

Author: Christian Seifert
Publisher: Springer Nature
ISBN: 3030893979
Category : Differential equations
Languages : en
Pages : 321

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Book Description
This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner. Moreover, the strength of this method is demonstrated by a large variety of examples, showing the applicability of the approach of evolutionary equations in various fields. Additionally, a quantitative theory for evolutionary equations is developed. The text is self-contained, providing an excellent source for a first study on evolutionary equations and a decent guide to the available literature on this subject, thus bridging the gap to state-of-the-art mathematical research.

Author: Delio Mugnolo
Publisher: Springer
ISBN: 3319046217
Category : Science
Languages : en
Pages : 286

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Book Description
This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations. Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations. This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to elliptic equations and related spectral problems. Moreover, for tackling the most general settings - e.g. encoded in the transmission conditions in the network nodes - one classical and elegant tool is that of operator semigroups. This book is simultaneously a very concise introduction to this theory and a handbook on its applications to differential equations on networks. With a more interdisciplinary readership in mind, full proofs of mathematical statements have been frequently omitted in favor of keeping the text as concise, fluid and self-contained as possible. In addition, a brief chapter devoted to the field of neurodynamics of the brain cortex provides a concrete link to ongoing applied research.

Author: Mi-Ho Giga
Publisher: Springer Nature
ISBN: 303134796X
Category : Mathematics
Languages : en
Pages : 163

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Book Description
This book addresses the issue of uniqueness of a solution to a problem – a very important topic in science and technology, particularly in the field of partial differential equations, where uniqueness guarantees that certain partial differential equations are sufficient to model a given phenomenon. This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establish its uniqueness. This book examines three very fundamental equations: ordinary differential equations, scalar conservation laws, and Hamilton-Jacobi equations. Starting from the standard Gronwall inequality, this book discusses less regular ordinary differential equations. It includes an introduction of advanced topics like the theory of maximal monotone operators as well as what is called DiPerna-Lions theory, which is still an active research area. For conservation laws, the uniqueness of entropy solution, a special (discontinuous) weak solution is explained. For Hamilton-Jacobi equations, several uniqueness results are established for a viscosity solution, a kind of a non-differentiable weak solution. The uniqueness of discontinuous viscosity solution is also discussed. A detailed proof is given for each uniqueness statement. The reader is expected to learn various fundamental ideas and techniques in mathematical analysis for partial differential equations by establishing uniqueness. No prerequisite other than simple calculus and linear algebra is necessary. For the reader’s convenience, a list of basic terminology is given at the end of this book.