General

The aim of this book is a detailed study of topological effects related to continuity of the dependence of solutions on initial values and parameters. This allows us to develop cheaply a theory which deals easily with equations having singularities and...

The new series, International Mathematical Series founded by Kluwer / Plenum Publishers and the Russian publisher, Tamara Rozhkovskaya is published simultaneously in English and in Russian and starts with two volumes dedicated to the famous Russian...

Beginning with the works of N.N.Krasovskii [81, 82, 83], which clari fied the functional nature of systems with delays, the functional approach provides a foundation for a complete theory of differential equations with delays. Based on the functional...

This volume provides a comprehensive review of the developments which have taken place during the last thirty years concerning the asymptotic properties of solutions of nonautonomous ordinary differential equations. The conditions of oscillation of...

In some domains of mechanics, physics and control theory boundary value problems arise for nonlinear first order PDEs. A well-known classical result states a sufficiency condition for local existence and uniqueness of twice differentiable solution. This...

Since the initiative works for global analysis of linear differential equations by G.G. Stokes and B. Riemann in 1857, the Airy function and the Gauss hypergeometric function became the most important and the greatest practical special functions, which...

This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type...

In this book we consider a Cauchy problem for a system of ordinary differential equations with a small parameter. The book is divided into th ree parts according to three ways of involving the small parameter in the system. In Part 1 we study the...

0.1 The partial differential equation (1) (Au)(x) = L aa(x)(Dau)(x) = f(x) m lal9 is called elliptic on a set G, provided that the principal symbol a2m(X, ) = L aa(x) a lal=2m of the operator A is invertible on G X (~n / 0); A is called elliptic on G,...

More than ten years have passed since the book of F. Bethuel, H. Brezis and F. H elein, which contributed largely to turning Ginzburg-Landau equations from a renowned physics model into a large PDE research ?eld, with an ever-increasing number of papers...

This text contains a collection of 28 contributions on the topics of bifurcation theory and dynamical systems, mostly from the point of view of symmetry breaking, which has been revealed to be a powerful tool in the understanding of pattern formation and...

This book has emerged from the study of a new concept in material science that has been realized about a decade ago. Before that, I had been working for more than 20 years on conventional composites assembled in space and therefore adjusted to optimal...

The Classical Theory of Integral Equations is a thorough, concise, and rigorous treatment of the essential aspects of the theory of integral equations. The book provides the background and insight necessary to facilitate a complete understanding of the...

Faculty of Engineering, University of Alberta; Faculty of Science, University of Alberta. As on previous occasions, advice and general guidance were provided by the International Steering Committee. The next IMSE conference will be held in August 2002 at...

This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in...

This book considers signal processing and physical modeling meth ods for sound synthesis. Such methods are useful for example in mu sic synthesizers, computer sound cards, and computer games. Physical modeling synthesis has been commercialized for the...

Homogenization is a method for modeling processes in microinhomogeneous media, which are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology. These processes are described...

Therearemanyexcellenttextsonelementarydi?erentialequationsdesignedfor the standard sophomore course. However, in spite of the fact that most courses are one semester in length, the texts have evolved into calculus-like pres- tations that include a large...

The 17 invited research articles in this volume, all written by leading experts in their respective fields, are dedicated to the great French mathematician Jean Leray. A wide range of topics with significant new results---detailed proofs---are presented...

The isomorphism problem of ergodic theory has been extensively studied since Kolmogorov's introduction of entropy into the subject and especially since Ornstein's solution for Bernoulli processes. Much of this research has been in the abstract...

This self-contained monograph traces the evolution of the limit-point/limit-circle problem from its 1910 inception, in a paper by Hermann Weyl, to its modern-day extensions to the asymptotic analysis of nonlinear differential equations. The authors...

The subject of local dynamical systems is concerned with the following two questions: 1. Given an nxn matrix A, describe the behavior, in a neighborhood of the origin, of the solutions of all systems of di?erential equations having a rest point at the...

Applied Delay Differential Equations is a friendly introduction to the fast-growing field of time-delay differential equations. Written to a multi-disciplinary audience, it sets each area of science in his historical context and then guides the reader...

The Institute for Mathematics and its Applications (IMA) devoted its 1997-1998 program to Emerging Applications of Dynamical Systems. Dynamical systems theory and related numerical algorithms provide powerful tools for studying the solution behavior of...

The original motivation of this study comes from the following questions that were mentioned to one ofus by H. Matano. Let 2 2 G= B = {x=(X1lX2) E 2; x~ + x~ = Ixl < 1}. 1 Consider the Ginzburg-Landau functional 2 2 (1) E~(u) = ~ LIVul + 4~2 L(lu1 _1)2...

In nonlinear problems, essentially new phenomena occur which have no place in the corresponding linear problems. Therefore, in the study of nonlinear problems the major purpose is not so much to introduce methods that improve the accuracy of linear...

The work of Hans Lewy (1904--1988) has had a profound influence in the direction of applied mathematics and partial differential equations, in particular, from the late 1920s. Two of the particulars are well known. The Courant--Friedrichs--Lewy condition...

* A comprehensive and systematic exposition of the properties of semiconcave functions and their various applications, particularly to optimal control problems, by leading experts in the field * A central role in the present work is reserved for the...

'Et moi, .... si j'avait su comment en revenir, One service mathematics has rendered the je n'y semis point all,,: human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded...

The International Conference on Differential Equations, theor*y, nu- merics and applications(ICDE'96-Bandung) was held successfully at the West Aula of Institut TeknoIogi Bandung on September 29 - October 2, 1996, hosted by the Center of Mathematics and...

Consists of expository articles and research papers highlighting new results on Carleman estimates and their applications. Focus is on unique continuation, control theory, and inverse problems. New results on strong uniqueness for second or higher order...

In the past several decades the classical Perron-Frobenius theory for nonnegative matrices has been extended to obtain remarkably precise and beautiful results for classes of nonlinear maps. This nonlinear Perron-Frobenius theory has found significant...

The title gives a reasonable ?rst-order approximation to what this book is about. To explain why, let's start with the expression "di?erential equations." These are essential in science and engineering, because the laws of nature t- ically result in...

The present monograph is devoted to the theory of the solvability in generalized functions of general boundary value problems of mathematieal physies. It is the eontinuation of the author's book [Rl], where elliptic boundary value problems have been...

Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This text is the first comprehensive exposition of the theory of semiconcave functions,...

This text is meant to be an introduction to critical point theory and its ap- plications to differential equations. It is designed for graduate and postgrad- uate students as well as for specialists in the fields of differential equations, variational...

This volume consists of papers presented in the special sessions on "Wave Phenomena and Related Topics", and "Asymptotics and Homogenization" of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997. The...

The present monograph is devoted to the complex theory of differential equations. Not yet a handbook, neither a simple collection of articles, the book is a first attempt to present a more or less detailed exposition of a young but promising branch of...

Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences is the main focus of this workbook. In a systematic introductory manner, this unique book deliniates...

In this book the author presents the Opial, Poincare, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for the above are derived using three different types of fractional derivatives, namely by Canavati, Riemann-Liouville...