Solution of Initial Value Problems in Classes of Generalized Analytic Functions - Softcover

Tutschke, Wolfgang

 
9783540502166: Solution of Initial Value Problems in Classes of Generalized Analytic Functions
Softcover
ISBN 10: 3540502165 ISBN 13: 9783540502166
Verlag: Springer, 1989

Inhaltsangabe

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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Reseña del editor

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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Verlag
Springer
Erscheinungsdatum
1989
Sprache
Englisch
ISBN 10 
3540502165
ISBN 13 
9783540502166
Einband
Tapa blanda
Anzahl der Seiten
192
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
CMN Printpool Inh. Mathis Neumann
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Hamburg
Deutschland

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Vorgestellte Ausgabe

ISBN 10:  0387502165 ISBN 13:  9780387502168
Verlag: Springer Verlag, 1989
Softcover