Homogenization of Differential Operators and Integral Functionals pdf epub mobi txt 电子书下载 2026

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出版者:Springer Verlag

作者:Jikov, V. V./ Kozlov, S. M./ Oleinik. O. A.

出品人:

页数:570

译者:G.A. Yosifian

出版时间:1994-11-1

价格:162

装帧:HRD

isbn号码:9780387548098

丛书系列:

图书标签:

数学
偏微分方程
均值化理论
积分泛函
函数空间
谱分析
渐近分析
边界层
数值分析
泛函分析
应用数学

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具体描述

It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape a s a distinct mathe matical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of non linear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogeniza tion problems for· partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each sep arate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the con stituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc.

这本书系统地探讨了物理学和数学领域中关于差分算子及其相关函数的研究，旨在为读者提供全面而深入的理论知识背景。内容涵盖了从基础概念到高级应用的多层次分析，详细描述了差分算子在不同维度中的行为与意义。书中着重介绍了该算子在微分方程解法、数值计算以及物理现象建模中的具体运用，通过丰富的案例研究帮助读者理解其应用价值。特别关注的是，作者不仅阐述了理论原理，还结合经典物理问题和现代技术，展示了差分算子在解决复杂问题时的重要作用。本书的结构清晰，分为多个章节，从基本定义出发，逐步深入探讨其数学特性及物理意义。在这一过程中，读者将系统了解到差分运算如何作为一种有效工具，帮助解析非连续或离散性的现象。内容还注重与其他相关学科的交叉联系，例如统计力学、信号处理以及计算数学等领域的关联，使得学习更为丰富多样。书中对各个理论部分均做了详细解释，同时提供了大量实用示例和实际应用场景，让读者能够灵活运用所学知识解决具体问题。这些内容不仅帮助理解抽象的数学概念，还培养了分析能力与逻辑思维。此外，作者在书中引入了最新研究进展和前沿应用，使得读者能够掌握当前领域的重要发展动态。通过丰富的理论讲解与多样的应用案例，这本书为读者打开了一扇深入探索数学与物理交互关系的大门，帮助其更好地理解复杂现象背后的机制。它不仅是一个知识的汇集，更是一场对逻辑与思维的挑战，为希望走入这一领域的人提供了坚实基础和宝贵参考。总体来说，这本书以严谨而有条理的方式，系统介绍了差分运算在数学和物理中的应用价值，其内容详尽且易于理解，对各相关学科研究者及学习者具有重要的指导意义。无论是初学者还是已有基础读者，都能从中获得丰富启发与宝贵知识。这份书不仅是一本科学著作，更是一份对思维方式和逻辑推理的培养工具。