Multiplication of Distributions A tool in mathematics, numerical eng
This book presents recent and very elementary developments of a theory of multiplication of distributions in the field of explicit and numerical solutions of systems of PDEs of physics (nonlinear elasticity, elastoplasticity, hydrodynamics, multifluid flo
- PDF / 10,498,009 Bytes
- 193 Pages / 468 x 684 pts Page_size
- 84 Downloads / 189 Views
1532
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg B. Eckmann, ZUrich F. Takens, Groningen
1532
Jean Francois Colombeau
Multiplication of Distributions A tool in mathematics, numerical engineering and theoretical physics
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest
Author Jean Francois Colombeau Ecole Normale Superieure de Lyon 46 Allee d'Italie F-69364 Lyon Cedex 07, France
Mathematics Subject Classification (1991): mHOS, 26E35, 30G99, 35A40, 35D05, 35L60,35R05,46FI0,65M05, 73D05, 76L05, 76T05
ISBN 3-540-56288-5 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-56288-5 Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1992 Printed in Germany
Typesetting: Camera ready by author Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 46/3140-543210 - Printed on acid-free paper
Introduction The aim of this book is to present a recent mathematical tool, in a way which is very accessible and free from mathematical techniques. The presentation developed here is in part heuristic, with emphasis on algebraic calculations and numerical recipes that can be easily used for numerical solutions of systems of equations modelling elasticity, elastoplasticity, hydrodynamics, acoustic diffusion, multifluid flows. This mathematical tool has also theoretical consequences such as convergence proofs for numerical schemes, existence - uniqueness theorems for solutions of systems of partial differential equations, unification of various methods for defining multiplications of distributions. These topics are not developed in this book since this would have made it not so elementary. A glimpse on these topics is given in two recent research expository papers: Colombeau [14] in Bull. of A.M.S. and Egorov [1] in Russian Math. Surveys. A detailed and careful self contained exposition on these mathematical applications can be found in Oberguggenberger's recent book [11] "Multiplication of distributions and applications to partial differential equations". A set of references is given concerning both the applied and the theoretical viewpoints. This book is the text of a course in numerical modelling given by the author to graduate students at the Ecole Normale Superieure de Lyon in the academic years 1989 - 90 and 1990 91. Many basic equations of physics contain, in more or less obvious or hidden ways, products looking like "ambiguous multiplications of dis
Data Loading...
