Nonlinear Semigroups and di erential equations in Banach spaces
Nonlinear Semigroups and di erential equations in Banach spaces
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DOI：
10.1007/978-94-010-1537-0
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发表时间：
1976-04
影响因子：
1.4
通讯作者：
V. Barbu
中科院分区：
文献类型：
--
作者：
V. Barbu
本书涉及 Banach 空间中收缩的非线性半群及其在与非线性耗散算子相关的微分方程的存在理论中的应用。非线性半群的研究源于对非线性抛物线方程的检验和各种非线性边值问题。 Y. Komura 所做的第一项工作激发了人们对这一主题的进一步研究和兴趣。由此开始了一系列研究，并由T. Kato、MG Crandall、A. Pazy、H. Brezis等人继续进行，他们为该理论的发展做出了重要贡献。下面发展的理论是单参数线性算子半群的 Hille-Yosida 理论的推广，并且是通过其方法或多或少松散地统一的多样化结果的集合。该理论也与非线性单调算子理论密切相关。当然，我们的阐述并不能涵盖这一理论的所有方面，并且为了简洁起见，对该主题的许多重要贡献都被排除在外。我们试图向读者展示基本结果并引导他们了解一些应用。本书旨在成为独立的。假定读者仅具备泛函分析、函数论和偏微分方程的基本知识。第一章总结了阅读本书的一些必要先决条件，无论是否有证据。
This book is concerned with nonlinear semigroups of contractions in Banach spaces and their application to the existence theory for differential equa tions associated with nonlinear dissipative operators. The study of nonlinear semi groups resulted from the examination of nonlinear parabolic equations and from various nonlinear boundary value problems. The first work done by Y. Komura stimulated much further work and interest in this subject. Thus a series of studies was begun and then continued by T. Kato, MG Crandall, A. Pazy, H. Brezis and others, who made important con tributions to the development of the theory. The theory as developed below is a generalisation of the Hille-Yosida theory for one-parameter semigroups of linear operators and is a collection of diversified results unified more or less loosely by their methods of approach. This theory is also closely related to the theory of nonlinear monotone operators. Of course not all aspects of this theory could be covered in our expo sition, and many important contributions to the subject have been excluded for the sake of brevity. We have attempted to present the basic results to the reader and to orient him toward some of the applications. This book is intended to be self-contained. The reader is assumed to have only a basic knowledge of functional analysis, function theory and partial differential equations. Some of the necessary prerequisites for the reading of this' book are summarized, with or without proof, in Chapter I.