Books in Partial differential equations

Second Order Linear Differential Equations in Banach Spaces

1st Edition
Volume 108
August 18, 2011
H.O. Fattorini
English
eBook
9 7 8 0 0 8 0 8 7 2 1 9 3

Second order linear differential equations in Banach spaces can be used for modelling such second order equations of mathematical physics as the wave equation, the Klein-Gordon equation, et al. In this way, a unified treatment can be given to subjects such as growth of solutions, singular perturbation of parabolic, hyperbolic and Schrödinger type initial value problems, and the like. The book covers in detail these subjects as well as the applications to each specific problem.

Transmutation Theory and Applications

1st Edition
Volume 117
August 18, 2011
R. Carroll
English
eBook
9 7 8 0 0 8 0 8 7 2 2 8 5

Recent Topics in Nonlinear PDE IV

1st Edition
Volume 160
April 1, 2000
M. Mimura + 1 more
English
eBook
9 7 8 0 0 8 0 8 8 0 2 0 4

This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences. Twelve papers present recent work in analysis, computational analysis of nonlinear PDEs and their applications.

Computer Solution of Large Linear Systems

1st Edition
Volume 28
June 16, 1999
Gerard Meurant
English
eBook
9 7 8 0 0 8 0 5 2 9 5 1 6

This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.

Fractional Differential Equations

1st Edition
Volume 198
October 21, 1998
Igor Podlubny
English
Hardback
9 7 8 0 1 2 5 5 8 8 4 0 9
eBook
9 7 8 0 0 8 0 5 3 1 9 8 4

This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models.In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications.

Multiscale Wavelet Methods for Partial Differential Equations

1st Edition
Volume 6
August 4, 1997
Wolfgang Dahmen + 2 more
English
eBook
9 7 8 0 0 8 0 5 3 7 1 4 6

This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource.

The Theory of Singular Perturbations

1st Edition
Volume 42
November 8, 1996
E.M. de Jager + 1 more
English
eBook
9 7 8 0 0 8 0 5 4 2 7 5 1

The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed.The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathematical justification of these methods. The latter implies a priori estimates of solutions of differential equations; this involves the application of Gronwall's lemma, maximum principles, energy integrals, fixed point theorems and Gåding's theorem for general elliptic equations. These features make the book of value to mathematicians and researchers in the engineering sciences, interested in the mathematical justification of formal approximations of solutions of practical perturbation problems. The text is selfcontained and each chapter is concluded with some exercises.

Algebraic and Analytic Methods in Representation Theory

1st Edition
Volume 17
September 27, 1996
Bent Orsted
English
eBook
9 7 8 0 0 8 0 5 2 6 9 5 9

This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike.

Analytic Element Modeling of Groundwater Flow

1st Edition
September 20, 1995
H. M. Haitjema
English
eBook
9 7 8 0 0 8 0 4 9 9 1 0 9

Modeling has become an essential tool for the groundwater hydrologist. Where field data is limited, the analytic element method (AEM) is rapidly becoming the modeling method of choice, especially given the availability of affordable modeling software. Analytic Element Modeling of Groundwater Flow provides all the basics necessary to approach AEM successfully, including a presentation of fundamental concepts and a thorough introduction to Dupuit-Forchheimerfl... This book is unique in its emphasis on the actual use of analytic element models. Real-world examples complement material presented in the text.An educational version of the analytic element program GFLOW is included to allow the reader to reproduce the various solutions to groundwater flow problems discussed in the text. Researchers and graduate students in groundwater hydrology, geology, andengineering will find this book an indispensable resource.

Geometric Measure Theory

2nd Edition
May 19, 2014
Frank Morgan
English
eBook
9 7 8 1 4 8 3 2 9 6 6 4 7

Geometric measure theory is the mathematical framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Morgan emphasizes geometry over proofs and technicalities, and includes a bibliography and abundant illustrations and examples. This Second Edition features a new chapter on soap bubbles as well as updated sections addressing volume constraints, surfaces in manifolds, free boundaries, and Besicovitch constant results. The text will introduce newcomers to the field and appeal to mathematicians working in the field.

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