Homogenization Of Some Partial Differential Operators And Integral Functionals

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Homogenization Of Differential Operators And Integral Functionals

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Author : V.V. Jikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Homogenization Of Differential Operators And Integral Functionals written by V.V. Jikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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 Some Partial Differential Operators And Integral Functionals

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Author : Peter Wall
language : en
Publisher:
Release Date : 1998

Homogenization Of Some Partial Differential Operators And Integral Functionals written by Peter Wall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

G Convergence And Homogenization Of Nonlinear Partial Differential Operators

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Author : A.A. Pankov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

G Convergence And Homogenization Of Nonlinear Partial Differential Operators written by A.A. Pankov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

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.

Some Asymptotic Problems In The Theory Of Partial Differential Equations

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Author : O. A. Oleĭnik
language : en
Publisher: Cambridge University Press
Release Date : 1996-03-21

Some Asymptotic Problems In The Theory Of Partial Differential Equations written by O. A. Oleĭnik and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-03-21 with Mathematics categories.

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.

Unbounded Functionals In The Calculus Of Variations

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Author : Luciano Carbone
language : en
Publisher: CRC Press
Release Date : 2019-06-13

Unbounded Functionals In The Calculus Of Variations written by Luciano Carbone and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-13 with Mathematics categories.

Over the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals of the calculus of variations. This advanced-level monograph addresses these issues by developing the framework of a gener

Harmonic Analysis And Partial Differential Equations

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Author : Anatoly Golberg
language : en
Publisher: Springer Nature
Release Date : 2023-03-25

Harmonic Analysis And Partial Differential Equations written by Anatoly Golberg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-25 with Mathematics categories.

Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Stochastic Analysis And Partial Differential Equations

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Author : Gui-Qiang Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Stochastic Analysis And Partial Differential Equations written by Gui-Qiang Chen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

This book is a collection of original research papers and expository articles from the scientific program of the 2004-05 Emphasis Year on Stochastic Analysis and Partial Differential Equations at Northwestern University. Many well-known mathematicians attended the events and submitted their contributions for this volume. Topics from stochastic analysis discussed in this volume include stochastic analysis of turbulence, Markov processes, microscopic lattice dynamics, microscopic interacting particle systems, and stochastic analysis on manifolds. Topics from partial differential equations include kinetic equations, hyperbolic conservation laws, Navier-Stokes equations, and Hamilton-Jacobi equations. A variety of methods, such as numerical analysis, homogenization, measure-theoretical analysis, entropy analysis, weak convergence analysis, Fourier analysis, and Ito's calculus, are further developed and applied. All these topics are naturally interrelated and represent a cross-section of the most significant recent advances and current trends and directions in stochastic analysis and partial differential equations. This volume is suitable for researchers and graduate students interested in stochastic analysis, partial differential equations, and related analysis and applications.

Nonlinear Partial Differential Equations And Their Applications

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Author : Doina Cioranescu
language : en
Publisher: Elsevier
Release Date : 2002-06-21

Nonlinear Partial Differential Equations And Their Applications written by Doina Cioranescu and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-06-21 with Mathematics categories.

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.

Function Spaces Interpolation Theory And Related Topics

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Author : Michael Cwikel
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22

Function Spaces Interpolation Theory And Related Topics written by Michael Cwikel and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.

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.