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Bibliographic Details

Title: Solution of Initial Value Problems in Classes of Generalized Analytic Functions
Publisher: Springer
Publication Date: 1989
Language: English
ISBN 10: 3540502165
ISBN 13: 9783540502166
Binding: Soft cover
Condition: Very Good

About this title

Synopsis

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.

Language Notes

Text: English
Introduction: French, German, Russian

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