Homogenization Of Differential Operators And Integral Functionals

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Homogenization of Differential Operators and Integral Functionals

Author : V.V. Jikov
Publisher : Springer Science & Business Media
ISBN 13 : 3642846599
Total Pages : 583 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Homogenization of Differential Operators and Integral Functionals by : V.V. Jikov

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.

Homogenization of Differential Operators and Integral Functionals

Author : V V Jikov
Publisher :
ISBN 13 : 9783642846601
Total Pages : 588 pages
Book Rating : 4.8/5 (466 download)

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Book Synopsis Homogenization of Differential Operators and Integral Functionals by : V V Jikov

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.

G-Convergence and Homogenization of Nonlinear Partial Differential Operators

Author : A.A. Pankov
Publisher : Springer Science & Business Media
ISBN 13 : 9401589577
Total Pages : 269 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis G-Convergence and Homogenization of Nonlinear Partial Differential Operators by : A.A. Pankov

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.

Homogenization of Multiple Integrals

Author : Andrea Braides
Publisher : Oxford University Press
ISBN 13 : 9780198502463
Total Pages : 322 pages
Book Rating : 4.5/5 (24 download)

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Book Synopsis Homogenization of Multiple Integrals by : Andrea Braides

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.

An Introduction to Γ-Convergence

Author : Gianni Dal Maso
Publisher : Springer Science & Business Media
ISBN 13 : 1461203279
Total Pages : 351 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis An Introduction to Γ-Convergence by : Gianni Dal Maso

Download or read book An Introduction to Γ-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:

Differential Equations, Mathematical Physics, and Applications: Selim Grigorievich Krein Centennial

Author : Peter Kuchment
Publisher : American Mathematical Soc.
ISBN 13 : 147043783X
Total Pages : 117 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Differential Equations, Mathematical Physics, and Applications: Selim Grigorievich Krein Centennial by : Peter Kuchment

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.

Nonlinear Analysis and Variational Problems

Author : Panos M. Pardalos
Publisher : Springer Science & Business Media
ISBN 13 : 1441901582
Total Pages : 502 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Nonlinear Analysis and Variational Problems by : Panos M. Pardalos

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.

Function Spaces, Interpolation Theory and Related Topics

Author : Michael Cwikel
Publisher : Walter de Gruyter
ISBN 13 : 3110198053
Total Pages : 473 pages
Book Rating : 4.1/5 (11 download)

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Book Synopsis Function Spaces, Interpolation Theory and Related Topics by : Michael Cwikel

Download or read book Function Spaces, Interpolation Theory and Related Topics written by Michael Cwikel and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Partial Differential Equations and Their Applications

Author : Doina Cioranescu
Publisher : Elsevier
ISBN 13 : 0080537677
Total Pages : 665 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Nonlinear Partial Differential Equations and Their Applications by : Doina Cioranescu

Download or read book Nonlinear Partial Differential Equations and Their Applications written by Doina Cioranescu and published by Elsevier. This book was released on 2002-06-21 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Integral Methods in Science and Engineering

Author : Christian Constanda
Publisher : Springer
ISBN 13 : 3030160777
Total Pages : 478 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Integral Methods in Science and Engineering by : Christian Constanda

Download or read book Integral Methods in Science and Engineering written by Christian Constanda and published by Springer. This book was released on 2019-07-18 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Evolution Equations, Semigroups and Functional Analysis

Author : Brunello Terreni
Publisher : Springer Science & Business Media
ISBN 13 : 9783764367916
Total Pages : 426 pages
Book Rating : 4.3/5 (679 download)

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Book Synopsis Evolution Equations, Semigroups and Functional Analysis by : Brunello Terreni

Download or read book Evolution Equations, Semigroups and Functional Analysis written by Brunello Terreni and published by Springer Science & Business Media. This book was released on 2002 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Effective Dynamics of Stochastic Partial Differential Equations

Author : Jinqiao Duan
Publisher : Elsevier
ISBN 13 : 0128012692
Total Pages : 283 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Effective Dynamics of Stochastic Partial Differential Equations by : Jinqiao Duan

Download or read book Effective Dynamics of Stochastic Partial Differential Equations written by Jinqiao Duan and published by Elsevier. This book was released on 2014-03-06 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Harmonic Analysis and Applications

Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
ISBN 13 : 1470461277
Total Pages : 345 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Harmonic Analysis and Applications by : Carlos E. Kenig

Download or read book Harmonic Analysis and Applications written by Carlos E. Kenig and published by American Mathematical Soc.. This book was released on 2020-12-14 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Getting Acquainted with Homogenization and Multiscale

Author : Leonid Berlyand
Publisher : Springer
ISBN 13 : 303001777X
Total Pages : 178 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Getting Acquainted with Homogenization and Multiscale by : Leonid Berlyand

Download or read book Getting Acquainted with Homogenization and Multiscale written by Leonid Berlyand and published by Springer. This book was released on 2018-11-22 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Some Asymptotic Problems in the Theory of Partial Differential Equations

Author : O. A. Oleĭnik
Publisher : Cambridge University Press
ISBN 13 : 9780521485371
Total Pages : 218 pages
Book Rating : 4.4/5 (853 download)

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Book Synopsis Some Asymptotic Problems in the Theory of Partial Differential Equations by : O. A. Oleĭnik

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.

Free and Moving Boundaries

Author : Roland Glowinski
Publisher : CRC Press
ISBN 13 : 1420011154
Total Pages : 474 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Free and Moving Boundaries by : Roland Glowinski

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

Applied Mathematical Analysis: Theory, Methods, and Applications

Author : Hemen Dutta
Publisher : Springer
ISBN 13 : 3319999184
Total Pages : 810 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Applied Mathematical Analysis: Theory, Methods, and Applications by : Hemen Dutta

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.