Partial Differential Equations of Parabolic Type
Title | Partial Differential Equations of Parabolic Type PDF eBook |
Author | Avner Friedman |
Publisher | Courier Corporation |
Pages | 369 |
Release | 2013-08-16 |
Genre | Mathematics |
ISBN | 0486318265 |
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.
New Difference Schemes for Partial Differential Equations
Title | New Difference Schemes for Partial Differential Equations PDF eBook |
Author | Allaberen Ashyralyev |
Publisher | Birkhäuser |
Pages | 453 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3034879229 |
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.
Linear and Quasi-linear Equations of Parabolic Type
Title | Linear and Quasi-linear Equations of Parabolic Type PDF eBook |
Author | Olʹga A. Ladyženskaja |
Publisher | American Mathematical Soc. |
Pages | 74 |
Release | 1988 |
Genre | Mathematics |
ISBN | 9780821815731 |
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.
Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type
Title | Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type PDF eBook |
Author | Samuil D. Eidelman |
Publisher | Birkhäuser |
Pages | 395 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3034878443 |
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.
Parabolic Equations with Irregular Data and Related Issues
Title | Parabolic Equations with Irregular Data and Related Issues PDF eBook |
Author | Claude Le Bris |
Publisher | Walter de Gruyter GmbH & Co KG |
Pages | 264 |
Release | 2019-06-17 |
Genre | Mathematics |
ISBN | 3110633140 |
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.
Integration of Equations of Parabolic Type by the Method of Nets
Title | Integration of Equations of Parabolic Type by the Method of Nets PDF eBook |
Author | V. K. Saul'Yev |
Publisher | Elsevier |
Pages | 365 |
Release | 2014-07-10 |
Genre | Mathematics |
ISBN | 1483155323 |
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.
Second Order Parabolic Differential Equations
Title | Second Order Parabolic Differential Equations PDF eBook |
Author | Gary M. Lieberman |
Publisher | World Scientific |
Pages | 472 |
Release | 1996 |
Genre | Mathematics |
ISBN | 9789810228835 |
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.