Download or read book Homogenization of Differential Operators and Integral Functionals written by V.V. Jikov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as 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.
Download or read book Homogenization of Differential Operators and Integral Functionals written by V V Jikov and published by . This book was released on 1994-09-08 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an extensive study of the theory of homogenization of partial differential equations. This theory has become increasingly important in the last two decades and it forms the basis for numerous branches of physics like the mechanics of composite and perforated materials, filtration and disperse media. The book contains new methods to study homogenization problems, which arise in mathematics, science and engineering. It provides the basis for new research devoted to these problems and it is the first comprehensive monograph in this field. It will become an indispensable reference for graduate students in mathematics, physics and engineering.
Download or read book G Convergence and Homogenization of Nonlinear Partial Differential Operators written by A.A. Pankov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various applications of the homogenization theory of partial differential equations resulted in the further development of this branch of mathematics, attracting an increasing interest of both mathematicians and experts in other fields. In general, the theory deals with the following: Let Ak be a sequence of differential operators, linear or nonlinepr. We want to examine the asymptotic behaviour of solutions uk to the equation Auk = f, as k ~ =, provided coefficients of Ak contain rapid oscillations. This is the case, e. g. when the coefficients are of the form a(e/x), where the function a(y) is periodic and ek ~ 0 ask~=. Of course, of oscillation, like almost periodic or random homogeneous, are of many other kinds interest as well. It seems a good idea to find a differential operator A such that uk ~ u, where u is a solution of the limit equation Au = f Such a limit operator is usually called the homogenized operator for the sequence Ak . Sometimes, the term "averaged" is used instead of "homogenized". Let us look more closely what kind of convergence one can expect for uk. Usually, we have some a priori bound for the solutions. However, due to the rapid oscillations of the coefficients, such a bound may be uniform with respect to k in the corresponding energy norm only. Therefore, we may have convergence of solutions only in the weak topology of the energy space.
Download or read book Homogenization of Multiple Integrals written by Andrea Braides and published by Oxford University Press. This book was released on 1998 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the mathematical theory of the homogenization of multiple integrals, this book describes the overall properties of such functionals with various applications ranging from cellular elastic materials to Riemannian metrics.
Download or read book An Introduction to Convergence written by Gianni Dal Maso and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Equations Mathematical Physics and Applications Selim Grigorievich Krein Centennial written by Peter Kuchment and published by American Mathematical Soc.. This book was released on 2019-07-22 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 733. Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union. The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in ordinary and partial differential equations, fluid dynamics, and various applications.
Download or read book Some Asymptotic Problems in the Theory of Partial Differential Equations written by O. A. Oleĭnik and published by Cambridge University Press. This book was released on 1996-03-21 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1993, Professor Oleinik was invited to give a series of lectures about her work in the area of partial differential equations. This book contains those lectures, and more.
Download or read book Free and Moving Boundaries written by Roland Glowinski and published by CRC Press. This book was released on 2007-06-06 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addressing algebraic problems found in biomathematics and energy, Free and Moving Boundaries: Analysis, Simulation and Control discusses moving boundary and boundary control in systems described by partial differential equations (PDEs). With contributions from international experts, the book emphasizes numerical and theoretical control of mo
Download or read book Applied Mathematical Analysis Theory Methods and Applications written by Hemen Dutta and published by Springer. This book was released on 2019-02-21 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses key aspects of recent developments in applied mathematical analysis and its use. It also highlights a broad range of applications from science, engineering, technology and social perspectives. Each chapter investigates selected research problems and presents a balanced mix of theory, methods and applications for the chosen topics. Special emphasis is placed on presenting basic developments in applied mathematical analysis, and on highlighting the latest advances in this research area. The book is presented in a self-contained manner as far as possible, and includes sufficient references to allow the interested reader to pursue further research in this still-developing field. The primary audience for this book includes graduate students, researchers and educators; however, it will also be useful for general readers with an interest in recent developments in applied mathematical analysis and applications.
Download or read book Nonlinear Analysis and Variational Problems written by Panos M. Pardalos and published by Springer Science & Business Media. This book was released on 2009-10-20 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.
Download or read book Functional Micro and Nanosystems written by Karl-Heinz Hoffmann and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 4th caesarium brought together world known experts reporting the state-of-the-art of Functional Micro-and Nanosystems. Its purpose was to identify and open up new research directions in this rapidly evolving new area and to discuss the potential with respect to applications in automotive, biochemical and information technology. Thin film technologies are an attractive approach to incorporate functional properties into micro- or nano-systems. The continuing development towards smaller structures is driven by the use of higher driving frequencies and thus smaller wavelengths, the growing integration of different functions, the higher degree of parallelism, and size requirements for the detection of bio-molecules. Hence this new technology opens up new possibilities in terms of high frequency wireless data transmission over long distances, sensors showing high spatial and time resolution and new devices to process biological, optical and electrical signals.
Download or read book Differential Equations on Manifolds and Mathematical Physics written by Vladimir M. Manuilov and published by Springer Nature. This book was released on 2022-01-21 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries. The conference was mainly dedicated to partial differential equations on manifolds and their applications in mathematical physics, geometry, topology, and complex analysis. The volume contains selected contributions by leading experts in these fields and presents the current state of the art in several areas of PDE. It will be of interest to researchers and graduate students specializing in partial differential equations, mathematical physics, topology, geometry, and their applications. The readers will benefit from the interplay between these various areas of mathematics.
Download or read book Mathematical Problems in Elasticity and Homogenization written by O.A. Oleinik and published by Elsevier. This book was released on 2009-06-15 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional analysis and the theory of partial differential equations, all results in this book are given detailed mathematical proof. It is expected that the results and methods presented in this book will promote further investigation of mathematical models for processes in composite and perforated media, heat-transfer, energy transfer by radiation, processes of diffusion and filtration in porous media, and that they will stimulate research in other problems of mathematical physics and the theory of partial differential equations.
Download or read book Singularly Perturbed Boundary Value Problems written by Matteo Dalla Riva and published by Springer Nature. This book was released on 2021-10-01 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains. The main purpose is to illustrate a method called Functional Analytic Approach, to describe the dependence of the solutions upon a singular perturbation parameter in terms of analytic functions. Here the focus is on domains with small holes and the perturbation parameter is the size of the holes. The book is the first introduction to the topic and covers the theoretical material and its applications to a series of problems that range from simple illustrative examples to more involved research results. The Functional Analytic Approach makes constant use of the integral representation method for the solutions of boundary value problems, of Potential Theory, of the Theory of Analytic Functions both in finite and infinite dimension, and of Nonlinear Functional Analysis. Designed to serve various purposes and readerships, the extensive introductory part spanning Chapters 1–7 can be used as a reference textbook for graduate courses on classical Potential Theory and its applications to boundary value problems. The early chapters also contain results that are rarely presented in the literature and may also, therefore, attract the interest of more expert readers. The exposition moves on to introduce the Functional Analytic Approach. A reader looking for a quick introduction to the method can find simple illustrative examples specifically designed for this purpose. More expert readers will find a comprehensive presentation of the Functional Analytic Approach, which allows a comparison between the approach of the book and the more classical expansion methods of Asymptotic Analysis and offers insights on the specific features of the approach and its applications to linear and nonlinear boundary value problems.
Download or read book Elliptic Equations An Introductory Course written by Michel Chipot and published by Springer Nature. This book was released on with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book New Trends in Stochastic Analysis and Related Topics written by Huaizhong Zhao and published by World Scientific. This book was released on 2012 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.
Download or read book Filtration in Porous Media and Industrial Application written by M.S. Espedal and published by Springer. This book was released on 2007-05-06 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the presentation of some flow problems in porous media having relevant industrial applications. The main topics covered are: the manufacturing of composite materials, the espresso coffee brewing process, the filtration of liquids through diapers, various questions about flow problems in oil reservoirs and the theory of homogenization. The aim is to show that filtration problems arising in very practical industrial context exhibit interesting and highly nontrivial mathematical aspects. Thus the style of the book is mathematically rigorous, but specifically oriented towards applications, so that it is intended for both applied mathematicians and researchers in various areas of technological interest. The reader is required to have a good knowledge of the classical theory of PDE and basic functional analysis.
