| 书目名称 | Solution of Initial Value Problems in Classes of Generalized Analytic Functions | | 编辑 | Wolfgang Tutschke | | 视频video | | | 图书封面 |  | | 描述 | 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 n | | 出版日期 | Book 1989 | | 关键词 | Banach Space; analytic function; banach spaces; derivative; differential equation; partial differential e | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-662-09943-8 | | isbn_softcover | 978-3-540-50216-6 | | isbn_ebook | 978-3-662-09943-8 | | copyright | Springer-Verlag Berlin Heidelberg 1989 |
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发表于 2025-3-21 18:08:15
