Homogenization Of Differential Operators And Integral Functionals

Author : V.V. Jikov,S.M. Kozlov,O.A. Oleinik
Publisher : Springer Science & Business Media
Page : 583 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642846595

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Homogenization of Differential Operators and Integral Functionals by V.V. Jikov,S.M. Kozlov,O.A. Oleinik Pdf

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.

Author : V V Jikov,S M Kozlov,O a Oleinik
Publisher : Unknown
Page : 588 pages
File Size : 51,6 Mb
Release : 1994-09-08
Category : Electronic
ISBN : 3642846602

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Homogenization of Differential Operators and Integral Functionals by V V Jikov,S M Kozlov,O a Oleinik Pdf

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.

Author : A.A. Pankov
Publisher : Springer Science & Business Media
Page : 269 pages
File Size : 55,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401589574

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G-Convergence and Homogenization of Nonlinear Partial Differential Operators by A.A. Pankov Pdf

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.

Author : Andrea Braides,Anneliese Defranceschi
Publisher : Oxford University Press
Page : 322 pages
File Size : 46,6 Mb
Release : 1998
Category : Mathematics
ISBN : 019850246X

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Homogenization of Multiple Integrals by Andrea Braides,Anneliese Defranceschi Pdf

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.

Author : Gianni Dal Maso
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461203278

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An Introduction to Γ-Convergence by Gianni Dal Maso Pdf

Author : Peter Kuchment,Evgeny Semenov
Publisher : American Mathematical Soc.
Page : 117 pages
File Size : 40,5 Mb
Release : 2019-07-22
Category : Differential equations
ISBN : 9781470437831

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Differential Equations, Mathematical Physics, and Applications: Selim Grigorievich Krein Centennial by Peter Kuchment,Evgeny Semenov Pdf

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.

Author : Panos M. Pardalos,Themistocles M. Rassias,Akhtar A. Khan
Publisher : Springer Science & Business Media
Page : 502 pages
File Size : 53,7 Mb
Release : 2009-10-20
Category : Business & Economics
ISBN : 9781441901583

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Nonlinear Analysis and Variational Problems by Panos M. Pardalos,Themistocles M. Rassias,Akhtar A. Khan Pdf

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.

Author : Michael Cwikel,Miroslav Englis,Alois Kufner,Lars-Erik Persson,Gunnar Sparr
Publisher : Walter de Gruyter
Page : 473 pages
File Size : 42,6 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110198058

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Function Spaces, Interpolation Theory and Related Topics by Michael Cwikel,Miroslav Englis,Alois Kufner,Lars-Erik Persson,Gunnar Sparr Pdf

This volume contains 16 refereed research articles on function spaces, interpolation theory and related fields. Topics covered: theory of function spaces, Hankel-type and related operators, analysis on bounded symmetric domains, partial differential equations, Green functions, special functions, homogenization theory, Sobolev embeddings, Coxeter groups, spectral theory and wavelets. The book will be of interest to both researchers and graduate students working in interpolation theory, function spaces and operators, partial differential equations and analysis on bounded symmetric domains.

Author : Doina Cioranescu,Jaques-Louis Lions
Publisher : Elsevier
Page : 665 pages
File Size : 49,6 Mb
Release : 2002-06-21
Category : Mathematics
ISBN : 9780080537672

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Nonlinear Partial Differential Equations and Their Applications by Doina Cioranescu,Jaques-Louis Lions Pdf

This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, operations research, fluids and continuum mechanics, nonlinear dynamics, meteorology and climate, homogenization and material science, numerical analysis and scientific computations The book is of interest to everyone from postgraduate, who wishes to follow the most recent progress in these fields.

Author : Christian Constanda,Paul Harris
Publisher : Springer
Page : 478 pages
File Size : 53,6 Mb
Release : 2019-07-18
Category : Mathematics
ISBN : 9783030160777

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Integral Methods in Science and Engineering by Christian Constanda,Paul Harris Pdf

This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. The chapters in this book are based on talks given at the Fifteenth International Conference on Integral Methods in Science and Engineering, held July 16-20, 2018 at the University of Brighton, UK, and are written by internationally recognized researchers. The topics addressed are wide ranging, and include: Asymptotic analysis Boundary-domain integral equations Viscoplastic fluid flow Stationary waves Interior Neumann shape optimization Self-configuring neural networks This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.

Author : Jinqiao Duan,Wei Wang
Publisher : Elsevier
Page : 283 pages
File Size : 50,6 Mb
Release : 2014-03-06
Category : Mathematics
ISBN : 9780128012697

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Effective Dynamics of Stochastic Partial Differential Equations by Jinqiao Duan,Wei Wang Pdf

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors’ experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations Solutions or hints to all Exercises

Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 45,7 Mb
Release : 2020-12-14
Category : Education
ISBN : 9781470461270

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Harmonic Analysis and Applications by Carlos E. Kenig Pdf

The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.

Author : Brunello Terreni
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 51,7 Mb
Release : 2002
Category : Mathematics
ISBN : 3764367911

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Evolution Equations, Semigroups and Functional Analysis by Brunello Terreni Pdf

Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi

Author : Leonid Berlyand,Volodymyr Rybalko
Publisher : Springer
Page : 178 pages
File Size : 50,7 Mb
Release : 2018-11-22
Category : Computers
ISBN : 9783030017774

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Getting Acquainted with Homogenization and Multiscale by Leonid Berlyand,Volodymyr Rybalko Pdf

The objective of this book is to navigate beginning graduate students in mathematics and engineering through a mature field of multiscale problems in homogenization theory and to provide an idea of its broad scope. An overview of a wide spectrum of homogenization techniques ranging from classical two-scale asymptotic expansions to Gamma convergence and the rapidly developing field of stochastic homogenization is presented. The mathematical proofs and definitions are supplemented with intuitive explanations and figures to make them easier to follow. A blend of mathematics and examples from materials science and engineering is designed to teach a mixed audience of mathematical and non-mathematical students.

Author : O. A. Oleĭnik
Publisher : Cambridge University Press
Page : 218 pages
File Size : 49,6 Mb
Release : 1996-03-21
Category : Mathematics
ISBN : 0521485371

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Some Asymptotic Problems in the Theory of Partial Differential Equations by O. A. Oleĭnik Pdf

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.