Description: Solution of Initial Value Problems in Classes of Generalized Analytic Functions, Paperback by Tutschke, Wolfgang, ISBN 3540502165, ISBN-13 9783540502166, Like New Used, Free shipping in the US 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 th 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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Book Title: Solution of Initial Value Problems in Classes of Generalized Anal
Number of Pages: 188 Pages
Publication Name: Solution of Initial Value Problems in Classes of Generalized Analytic
Language: English
Publisher: Springer Berlin / Heidelberg
Publication Year: 1989
Subject: Differential Equations / General, Physics / Mathematical & Computational, Complex Analysis, Mathematical Analysis
Type: Textbook
Item Weight: 7.9 Oz
Subject Area: Mathematics, Science
Author: Wolfgang Tutschke
Format: Trade Paperback