Solution of Initial Value Problems in Classes of Generalized Analytic Functions

Name: Solution of Initial Value Problems in Classes of Generalized Analytic Functions
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 9783540502166
Price: 214.72 PLN
Availability: InStock

Autor: Wolfgang Tutschke

Język:

Oprawa: Miękka

Wydawca: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

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The purpose of the present book is to solve initial value problems in classes of generalized analyti...

Informacje o książce

Autor

Wolfgang Tutschke

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

1989

strony

188

EAN

9783540502166

ISBN

3540502165

Enbook ID

02006910

Wydawca

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Waga

224

Wymiary

133 x 203 x 11

Pełny opis

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.

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