Solution of Initial Value Problems in Classes of Generalized Analytic Functions

Language: English

Published by Springer Berlin Heidelberg, Springer Spektrum Mär 1989, 1989

3540502165 / 9783540502166

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This item is printed on demand - Print on Demand Titel. Neuware -The purpose of the present book is to solve initial value problems in classes of generalized analytic functions as well as to explain the functional-analytic background material in detail. From the point of view of the theory of partial differential equations the book is intend ed to generalize the classicalCauchy-Kovalevskayatheorem, whereas the functional-analytic background connected with the method of successive approximations and the contraction-mapping principle leads to the con cept of so-called scales of Banach spaces: 1. The method of successive approximations allows to solve the initial value problem du CTf = f(t,u), (0. 1) u(O) = u , (0. 2) 0 where u = u(t) ist real o. r vector-valued. It is well-known that this method is also applicable if the function u belongs to a Banach space. A completely new situation arises if the right-hand side f(t,u) of the differential equation (0. 1) depends on a certain derivative Du of the sought function, i. e. , the differential equation (0,1) is replaced by the more general differential equation du dt = f(t,u,Du), (0. 3) There are diff. erential equations of type (0. 3) with smooth right-hand sides not possessing any solution to say nothing about the solvability of the initial value problem (0,3), (0,2), Assume, for instance, that the unknown function denoted by w is complex-valued and depends not only on the real variable t that can be interpreted as time but also on spacelike variables x and y, Then the differential equation (0.Springer-Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 192 pp. Englisch.

Seller Inventory # 9783540502166

Title
Solution of Initial Value Problems in Classes of Generalized Analytic Functions
Author
Wolfgang Tutschke
Publisher
Springer Berlin Heidelberg, Springer Spektrum Mär 1989
Publication year
1989
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3540502165
ISBN 13
9783540502166
Item weight
223 grams
Dimensions
203x133x11 mm

buchversandmimpf2000

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