Solution of Initial Value Problems in Classes of Generalized Analytic Functions

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9783540502166: Solution of Initial Value Problems in Classes of Generalized Analytic Functions

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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