Nonlinear Evolution Operators and Semigroups Applications to Partial
This research monograph deals with nonlinear evolution operators and semigroups generated by dissipative (accretive), possibly multivalued operators, as well as with the application of this theory to partial differential equations. It shows that a large c
- PDF / 17,784,280 Bytes
- 292 Pages / 468 x 684 pts Page_size
- 72 Downloads / 218 Views
1260
Nicolae H. Pavel
Nonlinear Evolution Operators and Semigroups Applications to Partial Differential Equations
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann
1260
Nicolae H. Pavel
Nonlinear Evolution Operators and Semigroups Applications to Partial Differential Equations
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Author
Nicolae H. Pavel Universitatea lasi, Facultatea de Matematica. 6600 lasi, Romania and The Ohio State University, Department of Mathematics 231 West 18th Avenue, Columbus, OH 43210, USA
Mathematics Subject Classification (1980): Primary: 35A07, 35A35, 35B45, 35C99,47H09 Secondary: 34G20, 39A 10, 65J 15 ISBN 3-540-17974-7 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-17974-7 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 other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1987 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
Preface. The first aim of this book is to present in a coherent way some of the fundamental results and recent research on nonlinear evolution operators and semigroups. The second aim is to show how to apply these abstract results to unify the treatment of several types of partial differential equations arising in physics (the heat equation, wave equation, Schrodinger equation, and so on). The motivation of this theory is clearly pointed out in the following quotation from: Autumn Course on Semigroups, Theory and Applications, held at the International Centre For Theoretical Physics, Trieste (Italy), 12 November 14 December 1984 (BrezisCrandall Kappel, Directors). "The last two decades have witnessed a tremendous use of semigroups and evolution equations techniques in solving problems related to PDE and FDE. This allows the treatment of PDE and FDE as suitable ODE in infinite dimensional Banach spaces. This method has considerably simplified and clarified the the proofs, and has unified the treatment of several different classes of differential equations. It has solved many problems that had been left open by previously known methods, and has been very succesful in dealing with discontinuous data and regularity." Chapter 1 deals with the construction and main properties of nonlinear evolution operator U(t, s) associated with a class of nonlinear (possible multivalued) operators A(t) with time dependent domain, satisfying Hypotheses H(2.1) and H(2.2) in Section 2. We al
Data Loading...
