## Solution of Initial Value Problems in Classes of Generalized Analytic Functions

### Tutschke, Wolfgang

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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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The main subject of this book is the generalization of the Cauchy-Kovalevska theorem. Solutions of initial value problems are given for the cases where the initial functions are generalized analytic functions. Two methods are employed in order to obtain the generalizations: the method of Banach space scales and a modification of W. Walters's elementary proof of the calssical theorem by Cauchy-Kovalevska. Students can use the book as an introduction and researchers can find in it , an summery of mew generalization of CauchyKovalevska problems.

Language Notes:

Text: English
Introduction: French, German, Russian

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Book Description Springer-Verlag Berlin and Heidelberg GmbH Co. KG, Germany, 1989. Paperback. Book Condition: New. 201 x 135 mm. Language: English . Brand New Book ***** Print on Demand *****.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. Bookseller Inventory # AAV9783540502166

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Book Description Springer. Paperback. Book Condition: New. Paperback. 188 pages. The main subject of this book is the generalization of the Cauchy-Kovalevska theorem. Solutions of initial value problems are given for the cases where the initial functions are generalized analytic functions. Two methods are employed in order to obtain the generalizations: the method of Banach space scales and a modification of W. Walterss elementary proof of the calssical theorem by Cauchy-Kovalevska. Students can use the book as an introduction and researchers can find in it , an summery of mew generalization of CauchyKovalevska problems. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Bookseller Inventory # 9783540502166

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