Books in Partial differential equations

Viability, Invariance and Applications

1st Edition
Volume 207
June 4, 2007
Ovidiu Carja + 2 more
English
eBook
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The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.The book includes the most important necessary and sufficient conditions for viability starting with Nagumo’s Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts.

Handbook of Differential Equations: Stationary Partial Differential Equations

1st Edition
Volume 4
May 3, 2007
Michel Chipot
English
eBook
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A collection of self contained state-of-the art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.

Handbook of Differential Equations: Evolutionary Equations

1st Edition
Volume 3
October 24, 2006
C.M. Dafermos + 1 more
English
Hardback
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eBook
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The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's.Articles will highlight the present as well as expected future directions of development of the field with particular emphasis on applications. The article by Ambrosio and Savaré discussesthe most recent development in the theory of gradient flow of probability measures. After an introduction reviewing the properties of the Wasserstein space and corresponding subdifferential calculus, applications are given to evolutionarypartial differential equations. The contribution of Herrero provides a description of some mathematical approaches developed to account for quantitative as well as qualitative aspects of chemotaxis. Particular attention is paid to the limits of cell'scapability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slim mold Dictyostelium discoideum on the other.The chapter written by Masmoudi deals with a rather different topic - examples of singular limits in hydrodynamics. This is nowadays a well-studied issue given the amount of new results based on the development of the existence theory for rather general systems of equations in hydrodynamics. The paper by DeLellis addreses the most recent results for the transport equations with regard to possible applications in the theory of hyperbolic systems of conservation laws. Emphasis is put on the development of the theory in the case when the governing field is only a BV function.The chapter by Rein represents a comprehensive survey of results on the Poisson-Vlasov system in astrophysics. The question of global stability of steady states is addressed in detail. The contribution of Soner is devoted to different representations of non-linear parabolic equations in terms of Markov processes. After a brief introduction on the linear theory, a class ofnon-linear equations is investigated, with applications to stochastic control and differential games.The chapter written by Zuazua presents some of the recent progresses done on the problem of controllabilty of partial differential equations. The applications include the linear wave and heat equations,parabolic equations with coefficients of low regularity, and some fluid-structure interaction models.

Student Solutions Manual to Boundary Value Problems

5th Edition
November 16, 2005
David L. Powers
English
Paperback
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eBook
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This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e. The SSM is available in print via PDF or electronically, and provides the student with the detailed solutions of the odd-numbered problems contained throughout the book.

Handbook of Differential Equations: Evolutionary Equations

1st Edition
Volume 2
October 5, 2005
C.M. Dafermos + 1 more
English
eBook
9 7 8 0 0 8 0 4 6 1 3 8 0

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.

Handbook of Differential Equations:Stationary Partial Differential Equations

1st Edition
Volume 2
August 19, 2005
Michel Chipot + 1 more
English
eBook
9 7 8 0 0 8 0 4 6 1 0 7 6

A collection of self contained, state-of-the-art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.Partial differential equations represent one of the most rapidly developing topics in mathematics. This is due to their numerous applications in science and engineering on the one hand and to the challenge and beauty of associated mathematical problems on the other.Key features:- Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field.

Half-Linear Differential Equations

1st Edition
Volume 202
July 6, 2005
Ondrej Dosly + 1 more
English
eBook
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The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferent... equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE’s with p-Laplacian, half-linear difference equations and various more general nonlinear differential equations.

Fast Multipole Methods for the Helmholtz Equation in Three Dimensions

1st Edition
January 27, 2005
Nail A Gumerov + 1 more
English
Hardback
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eBook
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This volume in the Elsevier Series in Electromagnetism presents a detailed, in-depth and self-contained treatment of the Fast Multipole Method and its applications to the solution of the Helmholtz equation in three dimensions. The Fast Multipole Method was pioneered by Rokhlin and Greengard in 1987 and has enjoyed a dramatic development and recognition during the past two decades. This method has been described as one of the best 10 algorithms of the 20th century. Thus, it is becoming increasingly important to give a detailed exposition of the Fast Multipole Method that will be accessible to a broad audience of researchers. This is exactly what the authors of this book have accomplished. For this reason, it will be a valuable reference for a broad audience of engineers, physicists and applied mathematicians.

Handbook of Differential Equations: Evolutionary Equations

1st Edition
Volume 1
August 24, 2004
C.M. Dafermos + 1 more
English
Hardback
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eBook
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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 estimatesA.Bressan: The front tracking method for systems of conservation lawsE.DiBenedetto, J.M.Urbano,V.Vespri: Current issues on singular and degenerate evolution equations;L.Hsiao, S.Jiang: Nonlinear hyperbolic-parabolic coupled systemsA.Lunardi: Nonlinear parabolic equations and systemsD.Serre:L1-st... 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: Stationary Partial Differential Equations

1st Edition
July 6, 2004
Michel Chipot + 1 more
English
Hardback
9 7 8 0 4 4 4 5 1 1 2 6 3
eBook
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The book could be a good companion for any graduate student in partial differential equations or in applied mathematics. Each chapter brings indeed new ideas and new techniques which can be used in these fields. The differents chapters can be read independently and are of great pedagogical value. The advanced researcher will find along the book the most recent achievements in various fields.

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Books in Partial differential equations

Viability, Invariance and Applications

Handbook of Differential Equations: Stationary Partial Differential Equations

Handbook of Differential Equations: Evolutionary Equations

Student Solutions Manual to Boundary Value Problems

Handbook of Differential Equations: Evolutionary Equations

Handbook of Differential Equations:Stationary Partial Differential Equations

Half-Linear Differential Equations

Fast Multipole Methods for the Helmholtz Equation in Three Dimensions

Handbook of Differential Equations: Evolutionary Equations

Handbook of Differential Equations: Stationary Partial Differential Equations