Kategoria BISAC: Mathematics >> Differential Equations - General

This text is well-designed with respect to the exposition from the preliminary to the more advanced and the applications interwoven throughout. It provides the essential foundations for the theory as well as the basic facts relating to almost periodicity. In six structured and self-contained chapters, the author unifies the treatment of various classes of almost periodic functions, while uniquely addressing oscillations and waves in the almost periodic case.

This is the first text to present the latest results in almost periodic oscillations and waves. The presentation level...

Systemes multi-echelles est une introduction a la problematique des systemes multi-echelles du point de vue du mathematicien applique. Il se compose d'une mosaique d'exemples de problemes issus de la physique au sens large qui presentent pour leur modelisation et leur simulation cette difficulte essentielle de comporter en leur sein des echelles de temps ou d'espace tres differentes.

Cet ouvrage applique les algorithmes a Regimes Glissants (RG) aux boucles industrielles de regulation et d'asservissement pilotees jusqu'a ce jour par les traditionnels PID et leurs variantes (RST, etc.). Le systeme reel a commander peut etre de nature variee, avoir des parties mal ou non modelisees, etre soumis a des perturbations. Les algorithmes numeriques robustes RG calculent une commande ayant une composante discontinue et donnent une evolution du point de fonctionnement du systeme boucle sur la surface de glissement (l'equation de la surface definit la dynamique du systeme boucle)....

Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation,...

This monograph presents recent and new ideas arising from the study of problems of planar fluid dynamics, and which are interesting from the point of view of geometric function theory and potential theory. the book is concerned with geometric problems for Hele-Shaw flows. Additionally, Hele-Shaw flows on parameter spaces are discussed, and connections with string theory are revealed. Assumes a graduate level understanding of real and complex analysis, and fluid mechanics.

Gunter Lumer was an outstanding mathematician whose works have great influence on the research community in mathematical analysis and evolution equations. He was at the origin of the breath-taking development the theory of semigroups saw after the pioneering book of Hille and Phillips from 1957. This volume contains invited contributions presenting the state of the art of these topics and reflecting the broad interests of Gunter Lumer.

This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on the occasion of their 65th birthday. The volume brings the reader to the border of research in differential equations, a fast evolving branch of mathematics that, besides being a main subject for mathematicians, is one of the mathematical tools most used both by scientists and engineers.

Numerous applications of rod structures in civil engineering, aircraft and spacecraft confirm the importance of the topic. On the other hand the majority of books on structural mechanics use some simplifying hypotheses; these hypotheses do not allow to consider some important effects, for instance the boundary layer effects near the points of junction of rods. So the question concerning the limits of applicability of structural mechanics hypotheses and the possibilities of their refinement arise. In this connection the asymptotic analysis of equations of mathematical physics, the equations...

In contrast to other books devoted to the averaging method and the method of integral manifolds, in the present book we study oscillation systems with many varying frequencies. In the process of evolution, systems of this type can pass from one resonance state into another. This fact considerably complicates the investigation of nonlinear oscillations.

In the present monograph, a new approach based on exact uniform estimates of oscillation integrals is proposed. On the basis of this approach, numerous completely new results on the justification of the averaging method and its...