Second Order Equations With Nonnegative Characteristic Form
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Second Order Equations With Nonnegative Characteristic Form
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Author : O. Oleinik
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Second Order Equations With Nonnegative Characteristic Form written by O. Oleinik 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.
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
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Author : O. A. Oleinik
language : en
Publisher:
Release Date : 1973
Second Order Equations With Nonnegative Characteristic Form written by O. A. Oleinik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.
Second Order Equations With Non Negative Characteristic Form
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Author : O. Oleinik
language : en
Publisher:
Release Date : 1973-11-01
Second Order Equations With Non Negative Characteristic Form written by O. Oleinik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-11-01 with categories.
Quasilinear Degenerate And Nonuniformly Elliptic And Parabolic Equations Of Second Order
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Author : A. V. Ivanov
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Quasilinear Degenerate And Nonuniformly Elliptic And Parabolic Equations Of Second Order written by A. V. Ivanov 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 1984 with Mathematics categories.
Differential Equations
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Author : O.A. Oleinik
language : en
Publisher: CRC Press
Release Date : 2019-08-16
Differential Equations written by O.A. Oleinik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-16 with Mathematics categories.
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.
Hp Version Discontinuous Galerkin Methods On Polygonal And Polyhedral Meshes
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Author : Andrea Cangiani
language : en
Publisher: Springer
Release Date : 2017-11-27
Hp Version Discontinuous Galerkin Methods On Polygonal And Polyhedral Meshes written by Andrea Cangiani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-27 with Mathematics categories.
Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages. This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen t-shapes, element-sizes, and element-orders is shown to deliver substantial computational gains in several practical scenarios.
Recent Advances In Scientific Computing And Partial Differential Equations
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Author : Stanley Osher
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Recent Advances In Scientific Computing And Partial Differential Equations written by Stanley Osher 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 2003 with Science categories.
The volume is from the proceedings of the international conference held in celebration of Stanley Osher's sixtieth birthday. It presents recent developments and exciting new directions in scientific computing and partial differential equations for time dependent problems and their interplay with other fields, such as image processing, computer vision and graphics. Over the past decade, there have been very rapid developments in the field. This volume emphasizes the strong interaction of advanced mathematics with real-world applications and algorithms. The book is suitable for graduate students and research mathematicians interested in scientific computing and partial differential equations.
Partial Differential Equations In China
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Author : Chaohao Gu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Partial Differential Equations In China written by Chaohao Gu 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.
In the past few years there has been a fruitful exchange of expertise on the subject of partial differential equations (PDEs) between mathematicians from the People's Republic of China and the rest of the world. The goal of this collection of papers is to summarize and introduce the historical progress of the development of PDEs in China from the 1950s to the 1980s. The results presented here were mainly published before the 1980s, but, having been printed in the Chinese language, have not reached the wider audience they deserve. Topics covered include, among others, nonlinear hyperbolic equations, nonlinear elliptic equations, nonlinear parabolic equations, mixed equations, free boundary problems, minimal surfaces in Riemannian manifolds, microlocal analysis and solitons. For mathematicians and physicists interested in the historical development of PDEs in the People's Republic of China.
The Mathematics Of Finite Elements And Applications X Mafelap 1999
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Author : J.R. Whiteman
language : en
Publisher: Elsevier
Release Date : 2000-06-26
The Mathematics Of Finite Elements And Applications X Mafelap 1999 written by J.R. Whiteman and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-26 with Technology & Engineering categories.
The tenth conference on The Mathematics of Finite Elements and Applications, MAFELAP 1999, was held at Brunel University during the period 22-25 June, 1999. This book seeks to highlight certain aspects of the state-of-the-art theory and applications of finite element methods of that time. This latest conference, in the MAFELAP series, followed the well established MAFELAP pattern of bringing together mathematicians, engineers and others interested in the field to discuss finite element techniques. In the MAFELAP context finite elements have always been interpreted in a broad and inclusive manner, including techniques such as finite difference, finite volume and boundary element methods as well as actual finite element methods. Twenty-six papers were carefully selected for this book out of the 180 presentations made at the conference, and all of these reflect this style and approach to finite elements. The increasing importance of modelling, in addition to numerical discretization, error estimation and adaptivity was also studied in MAFELAP 1999.
Elliptic Boundary Value Problems Of Second Order In Piecewise Smooth Domains
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Author : Michail Borsuk
language : en
Publisher: Elsevier
Release Date : 2006-01-12
Elliptic Boundary Value Problems Of Second Order In Piecewise Smooth Domains written by Michail Borsuk and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-12 with Mathematics categories.
The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points. Key features: * New the Hardy – Friedrichs – Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation. * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this. * The question about the influence of the coefficients smoothness on the regularity of solutions. * New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points. * The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems. * The behaviour of weak solutions near conical point for the Dirichlet problem for m – Laplacian. * The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration. * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this. * The question about the influence of the coefficients smoothness on the regularity of solutions. * New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points. * The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems. * The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian. * The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.