{"product_id":"solution-of-initial-value-problems-in-classes-of-generalized-analytic-functions-9783540502166","title":"Solution of Initial Value Problems in Classes of Generalized Analytic Functions","description":"\u003cp\u003e • Author(s): Wolfgang Tutschke\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Differential Equations - General\u003c\/p\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","brand":"Springer","offers":[{"title":"Paperback","offer_id":47615203934359,"sku":"9783540502166","price":5627.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783540502166.webp?v=1775098763","url":"https:\/\/atlanticbooks.com\/products\/solution-of-initial-value-problems-in-classes-of-generalized-analytic-functions-9783540502166","provider":"Atlantic Books","version":"1.0","type":"link"}