Kategoria BISAC: Mathematics >> Differential Equations - General

The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements. This volume provides an up-to-date overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws. The captivating volume contains surveys of recent deep results and provides an overview of further developments and related open problems. Readers should have basic knowledge of PDE and measure theory.

This volume introduces an entirely new pseudodifferential analysis on the line, the opposition of which to the usual (Weyl-type) analysis can be said to reflect that, in representation theory, between the representations from the discrete and from the (full, non-unitary) series, or that between modular forms of the holomorphic and substitute for the usual Moyal-type brackets. This pseudodifferential analysis relies on the one-dimensional case of the recently introduced anaplectic representation and analysis, a competitor of the metaplectic representation and usual analysis.

Besides...

Dieses zweibandige Lehrbuch stellt das Gesamtgebiet der partiellen Differentialgleichungen - vom elliptischen, parabolischen und hyperbolischen Typ - in zwei und mehreren Veranderlichen vor. Im vorliegenden ersten Band werden folgende Themen behandelt: Integration auf Mannigfaltigkeiten, funktionalanalytische Grundlagen, Brouwerscher Abbildungsgrad, verallgemeinerte analytische Funktionen, Potentialtheorie und Kugelfunktionen, lineare partielle Differentialgleichungen. Wahrend in diesem Band die partiellen Differentialgleichungen mit Integraldarstellungen gelost werden, sollen im nachsten...

Cet ouvrage presente les modeles d'interaction onde-matiere faisant intervenir une description quantique de la matiere (optique quantique), ainsi que des modeles classiques qui en sont derives. L'objectif est de decrypter pour des lecteurs mathematiciens ces modeles habituellement decrits dans des livres de physique et de donner les resultats mathematiques et les methodes numeriques existants.

The framework of 'symmetry' provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications.

From the reviews:

" The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS

The aim of this volume that presents lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to biology and medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important...

Dieses Lehrbuch liefert eine elementare, auch fur Studierende der Ingenieurwissenschaften geeignete Einfuhrung in die grundlegenden numerischen Verfahren zur Losung von Anfangs- und Randwertaufgaben fur gewohnliche Differentialgleichungen. Das Studium der Inhalte wird durch erganzende Modellbeispiele sowie zahlreiche theoretische und numerische Ubungsaufgaben mit Losungshinweisen erleichtert. Ein kurzer Abschnitt liefert die notwendigen Grundlagen zur Theorie der gewohnlichen Differentialgleichungen.

Un systeme dynamique discret est un ensemble fini d'elements, prenant chacun un nombre fini d'etats, et evoluant, dans un temps discret, par interactions mutuelles. Ce livre est consacre a l'analyse de la dynamique temporelle de tels systemes. Grace a des outils de metrique discrete, on etablit des resultats de convergence globale (contraction booleenne) convergence locale vers un point fixe ou vers un cycle, et ceci pour differents modes operatoires.

Using a computational algebra approach, this comprehensive text addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The book gives the main properties of ideals in polynomial rings and their affine varieties followed by a discussion on the theory of normal forms and stability of differential equations. It contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography, making it a suitable graduate textbook as well as research...