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| Author | : Avner Friedman |
| Publisher | : Courier Corporation |
| Total 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.
| Author | : Allaberen Ashyralyev |
| Publisher | : Birkhäuser |
| Total 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.
| Author | : Olʹga A. Ladyženskaja |
| Publisher | : American Mathematical Soc. |
| Total 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.
| Author | : E. M. Landis |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 224 |
| Release | : 1997-12-02 |
| Genre | : Mathematics |
| ISBN | : 9780821897812 |
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 | : Samuil D. Eidelman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 406 |
| Release | : 2004-09-27 |
| Genre | : Mathematics |
| ISBN | : 9783764371159 |
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 |
| Total 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.
| Author | : Avner Friedman |
| Publisher | : Courier Corporation |
| Total Pages | : 276 |
| Release | : 2008-11-24 |
| Genre | : Mathematics |
| ISBN | : 0486469190 |
Largely self-contained, this three-part treatment focuses on elliptic and evolution equations, concluding with a series of independent topics directly related to the methods and results of the preceding sections. 1969 edition.
| Author | : Claude Le Bris |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 242 |
| 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.
| Author | : Walter A. Strauss |
| Publisher | : John Wiley & Sons |
| Total Pages | : 467 |
| Release | : 2007-12-21 |
| Genre | : Mathematics |
| ISBN | : 0470054565 |
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 | : Stig Larsson |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 263 |
| Release | : 2008-12-05 |
| Genre | : Mathematics |
| ISBN | : 3540887059 |
The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.
