Background
Oleinik, Olga Arsenievna was born on July 2, 1925 in Matusov, Kiev, Ukraine. Daughter of Arseniy Ivanovich and Anna Petrovna Oleinik.
(Second order equations with nonnegative characteristic fo...)
Second order equations with nonnegative characteristic form constitute a new branch of the theory of partial differential equations, having arisen within the last 20 years, and having undergone a particularly intensive development in recent years. An equation of the form (1) is termed an equation of second order with nonnegative characteristic form on a set G, kj if at each point x belonging to G we have a (xHk~j ~ 0 for any vector ~ = (~l' ... '~m)' In equation (1) it is assumed that repeated indices are summed from 1 to m, and x = (x l' ••• , x ). Such equations are sometimes also called degenerating m elliptic equations or elliptic-parabolic equations. This class of equations includes those of elliptic and parabolic types, first order equations, ultraparabolic equations, the equations of Brownian motion, and others. The foundation of a general theory of second order equations with nonnegative characteristic form has now been established, and the purpose of this book is to pre sent this foundation. Special classes of equations of the form (1), not coinciding with the well-studied equations of elliptic or parabolic type, were investigated long ago, particularly in the paper of Picone 105, published some 60 years ago.
http://www.amazon.com/gp/product/1468489674/?tag=2022091-20
(Second order equations with nonnegative characteristic fo...)
Second order equations with nonnegative characteristic form constitute a new branch of the theory of partial differential equations, having arisen within the last 20 years, and having undergone a particularly intensive development in recent years. An equation of the form (1) is termed an equation of second order with nonnegative characteristic form on a set G, kj if at each point x belonging to G we have a (xHk~j ~ 0 for any vector ~ = (~l' ... '~m)' In equation (1) it is assumed that repeated indices are summed from 1 to m, and x = (x l' ••• , x ). Such equations are sometimes also called degenerating m elliptic equations or elliptic-parabolic equations. This class of equations includes those of elliptic and parabolic types, first order equations, ultraparabolic equations, the equations of Brownian motion, and others. The foundation of a general theory of second order equations with nonnegative characteristic form has now been established, and the purpose of this book is to pre sent this foundation. Special classes of equations of the form (1), not coinciding with the well-studied equations of elliptic or parabolic type, were investigated long ago, particularly in the paper of Picone 105, published some 60 years ago.
http://www.amazon.com/gp/product/0306307510/?tag=2022091-20
(This monograph is based on research undertaken by the aut...)
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.
http://www.amazon.com/gp/product/0444558365/?tag=2022091-20
Oleinik, Olga Arsenievna was born on July 2, 1925 in Matusov, Kiev, Ukraine. Daughter of Arseniy Ivanovich and Anna Petrovna Oleinik.
Degree, Moscow U., 1947; D in Mathematics, Moscow U., 1954; D (honorary), Rome U., 1981.
Professor mathematics, Moscow U., since 1955; head chair differential equations, Moscow U., since 1972.
(Second order equations with nonnegative characteristic fo...)
(Second order equations with nonnegative characteristic fo...)
(This monograph is based on research undertaken by the aut...)
Member Russian Academy Science, Royal Society Edinburgh (honorary), American Mathematics Society, International Society Interaction Mathematics and Mechanics, Academy Nazionale dei Lincei, Academy di Palermo, Institute Lombardo, Sächsische Akademie der Wissenschaften.
Married Lev Chudov; 1 child, Dmitriy.