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Author : Avner Friedman
Publisher : Courier Corporation
Page : 369 pages
File Size : 48,8 Mb
Release : 2013-08-16
Category : Mathematics
ISBN : 9780486318264
With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.
Author : Allaberen Ashyralyev,Pavel E. Sobolevskii
Publisher : Birkhäuser
Page : 453 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879224
This book explores new difference schemes for approximating the solutions of regular and singular perturbation boundary-value problems for PDEs. The construction is based on the exact difference scheme and Taylor's decomposition on the two or three points, which permits investigation of differential equations with variable coefficients and regular and singular perturbation boundary value problems.
Author : Claude Le Bris,Pierre-Louis Lions
Publisher : Walter de Gruyter GmbH & Co KG
Page : 264 pages
File Size : 40,5 Mb
Release : 2019-06-17
Category : Mathematics
ISBN : 9783110633146
This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.
Author : Olʹga A. Ladyženskaja,Vsevolod Alekseevich Solonnikov
Publisher : American Mathematical Soc.
Page : 74 pages
File Size : 41,9 Mb
Release : 1988
Category : Mathematics
ISBN : 0821815733
Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.
Author : Samuil D. Eidelman,Stepan D. Ivasyshen,Anatoly N. Kochubei
Publisher : Birkhäuser
Page : 390 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878449
This book is devoted to new classes of parabolic differential and pseudo-differential equations extensively studied in the last decades, such as parabolic systems of a quasi-homogeneous structure, degenerate equations of the Kolmogorov type, pseudo-differential parabolic equations, and fractional diffusion equations. It will appeal to mathematicians interested in new classes of partial differential equations, and physicists specializing in diffusion processes.
Author : Gary M. Lieberman
Publisher : World Scientific
Page : 472 pages
File Size : 50,7 Mb
Release : 1996
Category : Mathematics
ISBN : 981022883X
Introduction. Maximum principles. Introduction to the theory of weak solutions. Hölder estimates. Existence, uniqueness, and regularity of solutions. Further theory of weak solutions. Strong solutions. Fixed point theorems and their applications. Comparison and maximum principles. Boundary gradient estimates. Global and local gradient bounds. Hölder gradient estimates and existence theorems. The oblique derivative problem for quasilinear parabolic equations. Fully nonlinear equations. Introduction. Monge-Ampère and Hessian equations.
Author : E. M. Landis
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 50,8 Mb
Release : 1997-12-02
Category : Mathematics
ISBN : 0821897810
Most books on elliptic and parabolic equations emphasize existence and uniqueness of solutions. By contrast, this book focuses on the qualitative properties of solutions. In addition to the discussion of classical results for equations with smooth coefficients (Schauder estimates and the solvability of the Dirichlet problem for elliptic equations; the Dirichlet problem for the heat equation), the book describes properties of solutions to second order elliptic and parabolic equations with measurable coefficients near the boundary and at infinity. The book presents a fine elementary introduction to the theory of elliptic and parabolic equations of second order. The precise and clear exposition is suitable for graduate students as well as for research mathematicians who want to get acquainted with this area of the theory of partial differential equations.
Author : V. K. Saul'Yev
Publisher : Elsevier
Page : 364 pages
File Size : 52,7 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483155326
International Series of Monographs in Pure and Applied Mathematics, Volume 54: Integration of Equations of Parabolic Type by the Method of Nets deals with solving parabolic partial differential equations using the method of nets. The first part of this volume focuses on the construction of net equations, with emphasis on the stability and accuracy of the approximating net equations. The method of nets or method of finite differences (used to define the corresponding numerical method in ordinary differential equations) is one of many different approximate methods of integration of partial differential equations. The other methods, and some based on newer equations, are described. By analyzing these newer methods, older and existing methods are evaluated. For example, the asymmetric net equations; the alternating method of using certain equations; and the method of mean arithmetic and multi-nodal symmetric method point out that when the accuracy needs to be high, the requirements for stability become more defined. The methods discussed are very theoretical and methodological. The second part of the book concerns the practical numerical solution of the equations posed in Part I. Emphasis is on the commonly used iterative methods that are programmable on computers. This book is suitable for statisticians and numerical analysts and is also recommended for scientists and engineers with general mathematical knowledge.
Author : Luca Lorenzi,Adbelaziz Rhandi
Publisher : CRC Press
Page : 350 pages
File Size : 44,6 Mb
Release : 2021-01-06
Category : Mathematics
ISBN : 9780429557668
Semigroups of Bounded Operators and Second-Order Elliptic and Parabolic Partial Differential Equations aims to propose a unified approach to elliptic and parabolic equations with bounded and smooth coefficients. The book will highlight the connections between these equations and the theory of semigroups of operators, while demonstrating how the theory of semigroups represents a powerful tool to analyze general parabolic equations. Features Useful for students and researchers as an introduction to the field of partial differential equations of elliptic and parabolic types Introduces the reader to the theory of operator semigroups as a tool for the analysis of partial differential equations
Author : Ionuţ Munteanu
Publisher : Springer
Page : 214 pages
File Size : 45,5 Mb
Release : 2019-02-15
Category : Science
ISBN : 9783030110994
This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this technique are wide ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard equations; and deterministic or stochastic semi-linear heat equations arising in biology, chemistry, and population dynamics modeling. The text provides answers to the following problems, which are of great practical importance: Designing the feedback law using a minimal set of eigenfunctions of the linear operator obtained from the linearized equation around the target state Designing observers for the considered control systems Constructing time-discrete controllers requiring only partial knowledge of the state After reviewing standard notations and results in functional analysis, linear algebra, probability theory and PDEs, the author describes his novel stabilization algorithm. He then demonstrates how this abstract model can be applied to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteady-states, and more. Boundary Stabilization of Parabolic Equations will be of particular interest to researchers in control theory and engineers whose work involves systems control. Familiarity with linear algebra, operator theory, functional analysis, partial differential equations, and stochastic partial differential equations is required.
Author : A Alvino,P Buonocore,V Ferone,E Giarrusso,G Trombetti,S Matarasso
Publisher : CRC Press
Page : 236 pages
File Size : 47,5 Mb
Release : 1996-05-15
Category : Mathematics
ISBN : 0582259703
This Research Note collects reports of the invited plenary addresses given during the conference Elliptic and Parabolic Partial Differential Equations and Applications held in Capri, Italy, 19-23 September 1994. The conference was devoted to new developments in partial differential equations of elliptic and parabolic type and to their applications in various fields.
Author : Lieberstein
Publisher : Academic Press
Page : 282 pages
File Size : 43,8 Mb
Release : 1972-11-07
Category : Computers
ISBN : 9780080956022
Theory of Partial Differential Equations
Author : O. Oleinik
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468489651
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.
Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 49,8 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Author : Prof. Dr. Pavol Quittner,Prof. Dr. Philippe Souplet
Publisher : Springer
Page : 719 pages
File Size : 41,7 Mb
Release : 2019-06-13
Category : Mathematics
ISBN : 9783030182229
This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics. The first edition of this book has become one of the standard references in the field. This second edition provides a revised text and contains a number of updates reflecting significant recent advances that have appeared in this growing field since the first edition.