Handbook Of Differential Equations Evolutionary Equations
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Handbook of Differential Equations: Evolutionary Equations by C.M. Dafermos,Eduard Feireisl Pdf
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.
Handbook of differential equations by M. Chipot,P. Quittner Pdf
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.
Handbook of Differential Equations by Michel Chipot,Pal Quittner Pdf
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.
Handbook of Differential Equations by Constantine M. Dafermos,Eduard Feireisl Pdf
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.
Handbook of Differential Equations: Evolutionary Equations by C.M. Dafermos,Eduard Feireisl Pdf
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 PDE’s: from theory to numerics
Handbook of Differential Equations: Evolutionary Equations by C.M. Dafermos,Milan Pokorny Pdf
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
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.
Handbook of Differential Equations by Daniel Zwillinger,Vladimir Dobrushkin Pdf
Through the previous three editions, Handbook of Differential Equations has proven an invaluable reference for anyone working within the field of mathematics, including academics, students, scientists, and professional engineers. The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations, as well as numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations. Included for nearly every method are: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition.
A Basic Guide to Uniqueness Problems for Evolutionary Differential Equations by Mi-Ho Giga,Yoshikazu Giga Pdf
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.
Textbook of Differential Equations: Evolutionary Equations by Xander Cooper Pdf
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.
Handbook of Exact Solutions for Ordinary Differential Equations by Valentin F. Zaitsev,Andrei D. Polyanin Pdf
Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handboo
Handbook of Dynamical Systems by A. Katok,B. Hasselblatt Pdf
This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey “Principal Structures of Volume 1A.The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations). . Written by experts in the field.. The coverage of ergodic theory in these two parts of Volume 1 is considerably more broad and thorough than that provided in other existing sources. . The final cluster of chapters discusses partial differential equations from the point of view of dynamical systems.
Nonlinear Evolution Equations and Painlev Test by W.-H. Steeb,N. Euler Pdf
This book is an edited version of lectures given by the authors at a seminar at the Rand Afrikaans University. It gives a survey on the Painlev test, Painlev property and integrability. Both ordinary differential equations and partial differential equations are considered.
Evolution Equations with a Complex Spatial Variable by Ciprian G Gal,Sorin G Gal,Jerome A Goldstein Pdf
This book investigates several classes of partial differential equations of real time variable and complex spatial variables, including the heat, Laplace, wave, telegraph, Burgers, Black–Merton–Scholes, Schrödinger and Korteweg–de Vries equations. The complexification of the spatial variable is done by two different methods. The first method is that of complexifying the spatial variable in the corresponding semigroups of operators. In this case, the solutions are studied within the context of the theory of semigroups of linear operators. It is also interesting to observe that these solutions preserve some geometric properties of the boundary function, like the univalence, starlikeness, convexity and spirallikeness. The second method is that of complexifying the spatial variable directly in the corresponding evolution equation from the real case. More precisely, the real spatial variable is replaced by a complex spatial variable in the corresponding evolution equation and then analytic and non-analytic solutions are sought. For the first time in the book literature, we aim to give a comprehensive study of the most important evolution equations of real time variable and complex spatial variables. In some cases, potential physical interpretations are presented. The generality of the methods used allows the study of evolution equations of spatial variables in general domains of the complex plane. Contents:Historical Background and MotivationHeat and Laplace Equations of Complex Spatial VariablesHigher-Order Heat and Laplace Equations with Complex Spatial VariablesWave and Telegraph Equations with Complex Spatial VariablesBurgers and Black–Merton–Scholes Equations with Complex Spatial VariablesSchrödinger-Type Equations with Complex Spatial VariablesLinearized Korteweg–de Vries Equations with Complex Spatial VariablesEvolution Equations with a Complex Spatial Variable in General Domains Readership: Graduates and researchers in partial differential equations and in classical analytical function theory of one complex variable. Key Features:For the first time in literature, the study of evolution equations of real time variable and complex spatial variables is madeThe study includes some of the most important classes of partial differential equations: heat, Laplace, wave, telegraph, Burgers, Black–Merton–Scholes, Schrodinger and Korteweg–de Vries equationsThe book is entirely based on the authors' own workKeywords:Evolution Equations of Complex Spatial Variables;Semigroup of Linear Operators;Complex Convolution Integrals;Heat;Laplace;Wave;Telegraph;Burgers;BlackâMertonâScholes;Schrodinger;Kortewegâde Vries Equations
A Stability Technique for Evolution Partial Differential Equations by Victor A. Galaktionov,Juan Luis Vázquez Pdf
* Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations. * Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs. * Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.
