O.A. Oleinik's Books

Mathematical Models in Boundary Layer Theory

By: V.N. Samokhin

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Mathematical Models in Boundary Layer Theory

By: V.N. Samokhin

Since Prandtl first suggested it in 1904, boundary layer theory has become a fundamental aspect of fluid dynamics. Although a vast literature exists for theoretical and experimental aspects of the theory, for the most part, mathematical studies can be found only in separate, scattered articles. Mathematical Models in Boundary Layer Theory offers the first systematic exposition of the mathematical methods and main results of the theory. Beginning with the basics, the authors detail the techniques and results that reveal the nature of the equations that govern the flow within boundary layers and ultimately describe the laws underlying the motion of fluids with small viscosity. They investigate the questions of existence and uniqueness of solutions, the stability of solutions with respect to perturbations, and the qualitative behavior of solutions and their asymptotics. Of particular importance for applications, they present methods for an approximate solution of the Prandtl system and a subsequent evaluation of the rate of convergence of the approximations to the exact solution. Written by the world's foremost experts on the subject, Mathematical Models in Boundary Layer Theory provides the opportunity to explore its mathematical studies and their importance to the nonlinear theory of viscous and electrically conducting flows, the theory of heat and mass transfer, and the dynamics of reactive and muliphase media. With the theory's importance to a wide variety of applications, applied mathematicians-especially those in fluid dynamics-along with engineers of aeronautical and ship design will undoubtedly welcome this authoritative, state-of-the-art treatise.

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528

Publisher

Routledge

Published Date

ISBN 10

1351433229

ISBN 13

9781351433228

Homogenization of Differential Operators and Integral Functionals

By: V.V. Jikov,S.M. Kozlov,O.A. Oleinik

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Homogenization of Differential Operators and Integral Functionals

By: V.V. Jikov,S.M. Kozlov,O.A. Oleinik

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.

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583

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642846599

ISBN 13

9783642846595

Differential Equations

By: O.A. Oleinik

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Differential Equations

By: O.A. Oleinik

Part II of the Selected Works of Ivan Georgievich Petrowsky, contains his major papers on second order Partial differential equations, systems of ordinary. Differential equations, the theory, of Probability, the theory of functions, and the calculus of variations. Many of the articles contained in this book have Profoundly, influenced the development of modern mathematics. Of exceptional value is the article on the equation of diffusion with growing quantity of the substance. This work has found extensive application in biology, genetics, economics and other branches of natural science. Also of great importance is Petrowsky's work on a Problem which still remains unsolved - that of the number of limit cycles for ordinary differential equations with rational right-hand sides.

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522

Publisher

CRC Press

Published Date

ISBN 10

1000725197

ISBN 13

9781000725193

Mathematical Problems in Elasticity and Homogenization

By: O.A. Oleinik,A.S. Shamaev,G.A. Yosifian

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Mathematical Problems in Elasticity and Homogenization

By: O.A. Oleinik,A.S. Shamaev,G.A. Yosifian

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.

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413

Publisher

Elsevier

Published Date

ISBN 10

0080875475

ISBN 13

9780080875477

Some Asymptotic Problems in the Theory of Partial Differential Equations

By: O. A. Oleĭnik

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Some Asymptotic Problems in the Theory of Partial Differential Equations

By: O. A. Oleĭnik

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.

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218

Publisher

Cambridge University Press

Published Date

ISBN 10

0521485371

ISBN 13

9780521485371

The Boundary Value Problems of Mathematical Physics

By: O.A. Ladyzhenskaya

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The Boundary Value Problems of Mathematical Physics

By: O.A. Ladyzhenskaya

In the present edition I have included "Supplements and Problems" located at the end of each chapter. This was done with the aim of illustrating the possibilities of the methods contained in the book, as well as with the desire to make good on what I have attempted to do over the course of many years for my students-to awaken their creativity, providing topics for independent work. The source of my own initial research was the famous two-volume book Methods of Mathematical Physics by D. Hilbert and R. Courant, and a series of original articles and surveys on partial differential equations and their applications to problems in theoretical mechanics and physics. The works of K. o. Friedrichs, which were in keeping with my own perception of the subject, had an especially strong influence on me. I was guided by the desire to prove, as simply as possible, that, like systems of n linear algebraic equations in n unknowns, the solvability of basic boundary value (and initial-boundary value) problems for partial differential equations is a consequence of the uniqueness theorems in a "sufficiently large" function space. This desire was successfully realized thanks to the introduction of various classes of general solutions and to an elaboration of the methods of proof for the corresponding uniqueness theorems. This was accomplished on the basis of comparatively simple integral inequalities for arbitrary functions and of a priori estimates of the solutions of the problems without enlisting any special representations of those solutions.

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Page Count

350

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475743173

ISBN 13

9781475743173

Spatial Anisotropy of Induced Optical Effects in Crystalline Materials

By: A. S. Andrushchak,O. A. Buryy,N. A. Andrushchak,N. M. Demyanyshyn

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Spatial Anisotropy of Induced Optical Effects in Crystalline Materials

By: A. S. Andrushchak,O. A. Buryy,N. A. Andrushchak,N. M. Demyanyshyn

This book addresses analytical descriptions and geometric representations of the spatial anisotropy of induced optical effects in crystalline materials of different symmetry classes, as well as experimental methods and apparatus for the comprehensive studies of electro-, piezo-, elasto- and acousto-optic phenomena in crystalline solids. It also details 3D analysis of the anisotropies of linear electro-optic, piezo-optic, elasto-optic, acoustic and acousto-optic properties of various crystalline materials and constructs indicative or extreme surfaces describing the anisotropy effect.

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Page Count

213

Publisher

Cambridge Scholars Publishing

Published Date

ISBN 10

1527512037

ISBN 13

9781527512030

Some Asymptotic Problems in the Theory of Partial Differential Equations

By: Olga Oleinik

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Some Asymptotic Problems in the Theory of Partial Differential Equations

By: Olga Oleinik

In this book, Professor Oleinik highlights her work in the area of partial differential equations. The book is divided into two parts: the first is devoted to the study of the asymptotic behavior at infinity of solutions of a class of nonlinear second order elliptic equations in unbounded and, in particular, cylindrical domains. The second contains the most recent results of the author in the theory of homogenization of partial differential equations and is concerned with questions about partially perforated domains and of solutions with rapidly alternating types of boundary conditions. Many of the results here have not appeared in book form before, and it sheds new light on the subject, raising many new ideas and open problems.

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Page Count

216

Publisher

Cambridge University Press

Published Date

ISBN 10

0521480833

ISBN 13

9780521480833

Differential Equations

By: O.A. Oleinik

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Differential Equations

By: O.A. Oleinik

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Page Count

514

Publisher

CRC Press

Published Date

ISBN 10

1000717372

ISBN 13

9781000717372

Mathematical Models in Boundary Layer Theory

By: O.A. Oleinik,V.N. Samokhin

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Mathematical Models in Boundary Layer Theory

By: O.A. Oleinik,V.N. Samokhin

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532

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CRC Press

Published Date

ISBN 10

1584880155

ISBN 13

9781584880158

Homogenization of Differential Operators and Integral Functionals

By: V.V. Jikov,S.M. Kozlov,O.A. Oleinik

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Homogenization of Differential Operators and Integral Functionals

By: V.V. Jikov,S.M. Kozlov,O.A. Oleinik

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583

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642846599

ISBN 13

9783642846595

Mathematical Problems in Elasticity and Homogenization

By: O.A. Oleinik,A.S. Shamaev,G.A. Yosifian

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Mathematical Problems in Elasticity and Homogenization

By: O.A. Oleinik,A.S. Shamaev,G.A. Yosifian

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.

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Page Count

413

Publisher

Elsevier

Published Date

ISBN 10

0080875238

ISBN 13

9780080875231

Book's by O.A. Oleinik

Mathematical Models in Boundary Layer Theory

Mathematical Models in Boundary Layer Theory

Homogenization of Differential Operators and Integral Functionals

Homogenization of Differential Operators and Integral Functionals

Differential Equations

Differential Equations

Mathematical Problems in Elasticity and Homogenization

Mathematical Problems in Elasticity and Homogenization

Some Asymptotic Problems in the Theory of Partial Differential Equations

Some Asymptotic Problems in the Theory of Partial Differential Equations

The Boundary Value Problems of Mathematical Physics

The Boundary Value Problems of Mathematical Physics

Spatial Anisotropy of Induced Optical Effects in Crystalline Materials

Spatial Anisotropy of Induced Optical Effects in Crystalline Materials

Some Asymptotic Problems in the Theory of Partial Differential Equations

Some Asymptotic Problems in the Theory of Partial Differential Equations

Differential Equations

Differential Equations

Mathematical Models in Boundary Layer Theory

Mathematical Models in Boundary Layer Theory

Homogenization of Differential Operators and Integral Functionals

Homogenization of Differential Operators and Integral Functionals

Mathematical Problems in Elasticity and Homogenization

Mathematical Problems in Elasticity and Homogenization

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