Author: O. Oleinik
Publisher: Springer Science & Business Media
ISBN: 1468489658
Category : Mathematics
Languages : en
Pages : 265
Book Description
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.
Second-Order Equations With Nonnegative Characteristic Form
Author: O. Oleinik
Publisher: Springer Science & Business Media
ISBN: 1468489658
Category : Mathematics
Languages : en
Pages : 265
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 1468489658
Category : Mathematics
Languages : en
Pages : 265
Book Description
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.
Second Order Equations with Nonnegative Characteristic Form
Author: O. A. Oleinik
Publisher:
ISBN: 9780608054629
Category :
Languages : en
Pages : 267
Book Description
Publisher:
ISBN: 9780608054629
Category :
Languages : en
Pages : 267
Book Description
Second-Order Equations with Non-Negative Characteristic Form
Author: O. Oleinik
Publisher:
ISBN: 9781468489668
Category :
Languages : en
Pages : 268
Book Description
Publisher:
ISBN: 9781468489668
Category :
Languages : en
Pages : 268
Book Description
Second Order Equations with Nonnegative Form
Author: O. A. Oleĭnik
Publisher:
ISBN:
Category :
Languages : en
Pages : 259
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 259
Book Description
Second order equations with nonnegative characteristic form (Upravnenija vtorogo porjadka s neotricatel'noj charakterističeskoj formoj, engl.)
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 259
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 259
Book Description
Properties of Nonnegative Solutions of Second-order Elliptic Equations and Their Adjoints
Author: Patricia Ellen Bauman
Publisher:
ISBN:
Category :
Languages : en
Pages : 320
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 320
Book Description
Elliptic Partial Differential Equations of Second Order
Author: David Gilbarg
Publisher: Springer Science & Business Media
ISBN: 9783540411604
Category : Mathematics
Languages : en
Pages : 544
Book Description
This work aims to be of interest to those who have to work with differential equations and acts either as a reference or as a book to learn from. The authors have made the treatment self-contained.
Publisher: Springer Science & Business Media
ISBN: 9783540411604
Category : Mathematics
Languages : en
Pages : 544
Book Description
This work aims to be of interest to those who have to work with differential equations and acts either as a reference or as a book to learn from. The authors have made the treatment self-contained.
Uniqueness/nonuniqueness for Nonnegative Solutions of Second Order Parabolic Equations of the Form Ut
Author: János Engländer
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
Book Description
Second Order Parabolic Differential Equations
Author: Gary M Lieberman
Publisher: World Scientific
ISBN: 9814498114
Category : Mathematics
Languages : en
Pages : 462
Book Description
This book is an introduction to the general theory of second order parabolic differential equations, which model many important, time-dependent physical systems. It studies the existence, uniqueness, and regularity of solutions to a variety of problems with Dirichlet boundary conditions and general linear and nonlinear boundary conditions by means of a priori estimates. The first seven chapters give a description of the linear theory and are suitable for a graduate course on partial differential equations. The last eight chapters cover the nonlinear theory for smooth solutions. They include much of the author's research and are aimed at researchers in the field. A unique feature is the emphasis on time-varying domains.
Publisher: World Scientific
ISBN: 9814498114
Category : Mathematics
Languages : en
Pages : 462
Book Description
This book is an introduction to the general theory of second order parabolic differential equations, which model many important, time-dependent physical systems. It studies the existence, uniqueness, and regularity of solutions to a variety of problems with Dirichlet boundary conditions and general linear and nonlinear boundary conditions by means of a priori estimates. The first seven chapters give a description of the linear theory and are suitable for a graduate course on partial differential equations. The last eight chapters cover the nonlinear theory for smooth solutions. They include much of the author's research and are aimed at researchers in the field. A unique feature is the emphasis on time-varying domains.
Quasilinear Degenerate and Nonuniformly Elliptic and Parabolic Equations of Second Order
Author: A. V. Ivanov
Publisher: American Mathematical Soc.
ISBN: 9780821830802
Category : Mathematics
Languages : en
Pages : 306
Book Description
Publisher: American Mathematical Soc.
ISBN: 9780821830802
Category : Mathematics
Languages : en
Pages : 306
Book Description