Books in Partial differential equations

Handbook of Differential Equations: Evolutionary Equations

1st Edition
Volume 5
April 29, 2009
C.M. Dafermos + 1 more
English
Hardback
9 7 8 0 4 4 4 5 3 2 2 2 0
eBook
9 7 8 0 0 8 0 9 3 2 5 9 0

Handbook of Differential Equations: Evolutionary Equations is the last text of a five-volume reference in mathematics and methodology. This volume follows the format set by the preceding volumes, presenting numerous contributions that reflect the nature of the area of evolutionary partial differential equations. The book is comprised of five chapters that feature the following: A thorough discussion of the shallow-equations theory, which is used as a model for water waves in rivers, lakes and oceans. It covers the issues of modeling, analysis and applications • Evaluation of the singular limits of reaction-diffusion systems, where the reaction is fast compared to the other processes; and applications that range from the theory of the evolution of certain biological processes to the phenomena of Turing and cross-diffusion instability Detailed discussion of numerous problems arising from nonlinear optics, at the high-frequency and high-intensity regime • Geometric and diffractive optics, including wave interactions Presentation of the issues of existence, blow-up and asymptotic stability of solutions, from the equations of solutions to the equations of linear and non-linear thermoelasticity Answers to questions about unique space, such as continuation and backward uniqueness for linear second-order parabolic equations. Research mathematicians, mathematics lecturers and instructors, and academic students will find this book invaluable

Partial Differential Equations and Boundary Value Problems with Maple

2nd Edition
March 23, 2009
George A. Articolo
English
eBook
9 7 8 0 0 8 0 8 8 5 0 6 3

Partial Differential Equations and Boundary Value Problems with Maple, Second Edition, presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours - an investment that provides substantial returns. Maple's animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations. This updated edition provides a quick overview of the software w/simple commands needed to get started. It includes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equations. It also incorporates an early introduction to Sturm-Liouville boundary problems and generalized eigenfunction expansions. Numerous example problems and end of each chapter exercises are provided.

Handbook of Differential Equations: Evolutionary Equations

1st Edition
Volume 4
August 19, 2008
C.M. Dafermos + 1 more
English
Hardback
9 7 8 0 4 4 4 5 3 0 3 4 9
eBook
9 7 8 0 0 8 0 9 3 1 9 7 5

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.

Handbook of Differential Equations: Stationary Partial Differential Equations

1st Edition
Volume 5
February 4, 2008
Michel Chipot
English
Hardback
9 7 8 0 4 4 4 5 3 2 1 7 6
eBook
9 7 8 0 0 8 0 5 5 7 3 1 1

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.

Stochastic Differential Equations and Applications

2nd Edition
December 30, 2007
X Mao
English
eBook
9 7 8 0 8 5 7 0 9 9 4 0 2

This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists.

Viability, Invariance and Applications

1st Edition
Volume 207
June 4, 2007
Ovidiu Carja + 2 more
English
eBook
9 7 8 0 0 8 0 5 2 1 6 6 4

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
9 7 8 0 0 8 0 5 2 1 8 3 1

Handbook of Differential Equations: Evolutionary Equations

1st Edition
Volume 3
October 24, 2006
C.M. Dafermos + 1 more
English
Hardback
9 7 8 0 4 4 4 5 2 8 4 8 3
eBook
9 7 8 0 0 8 0 4 6 5 6 5 4

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
9 7 8 0 1 2 0 8 8 5 8 6 2
eBook
9 7 8 0 0 8 0 9 1 6 7 3 6

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.

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Books in Partial differential equations

Handbook of Differential Equations: Evolutionary Equations

Partial Differential Equations and Boundary Value Problems with Maple

Handbook of Differential Equations: Evolutionary Equations

Handbook of Differential Equations: Stationary Partial Differential Equations

Stochastic Differential Equations and Applications

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