{"product_id":"9783540502166","title":"Solution of Initial Value Problems in Classes of Generalized Analytic Functions","description":"\u003ch1\u003eSolution of Initial Value Problems in Classes of Generalized Analytic Functions\u003c\/h1\u003e \u003ch2\u003eTutschke, Wolfgang\u003c\/h2\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1989-03-30\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783540502166\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-662-09943-8\u003c\/p\u003e \u003cp\u003eDimensions: cm xcm\u003c\/p\u003e \u003cp\u003ePages: 188\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":46312629534860,"sku":"9783540502166","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783540502166.jpg?v=1771527865","url":"https:\/\/lateknightbooks.com\/products\/9783540502166","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}