Elliptic and Parabolic Equations with Discontinuous Coefficients
Elliptic and Parabolic Equations with Discontinuous Coefficients

Author: Antonino Maugeri

Publisher: Wiley-VCH

Published: 2000-12-13

Total Pages: 266

ISBN-13:

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This book unifies the different approaches in studying elliptic and parabolic partial differential equations with discontinuous coefficients. To the enlarging market of researchers in applied sciences, mathematics and physics, it gives concrete answers to questions suggested by non-linear models. Providing an up-to date survey on the results concerning elliptic and parabolic operators on a high level, the authors serve the reader in doing further research. Being themselves active researchers in the field, the authors describe both on the level of good examples and precise analysis, the crucial role played by such requirements on the coefficients as the Cordes condition, Campanato's nearness condition, and vanishing mean oscillation condition. They present the newest results on the basic boundary value problems for operators with VMO coefficients and non-linear operators with discontinuous coefficients and state a lot of open problems in the field.

Lectures on Elliptic and Parabolic Equations in Holder Spaces
Lectures on Elliptic and Parabolic Equations in Holder Spaces

Author: Nikolaĭ Vladimirovich Krylov

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 178

ISBN-13: 082180569X

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These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in H older spaces. Krylov shows that this theory - including some issues of the theory of nonlinear equations - is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed. This book, containing 200 exercises, aims to provide a good understanding of what kind of results are available and what kinds of techniques are used to obtain them.

Second Order Equations of Elliptic and Parabolic Type
Second Order Equations of Elliptic and Parabolic Type

Author: E. M. Landis

Publisher: American Mathematical Soc.

Published: 1997-12-02

Total Pages: 224

ISBN-13: 9780821897812

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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.

Numerical Methods for Elliptic and Parabolic Partial Differential Equations
Numerical Methods for Elliptic and Parabolic Partial Differential Equations

Author: Peter Knabner

Publisher: Springer Science & Business Media

Published: 2003-06-26

Total Pages: 437

ISBN-13: 038795449X

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This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

Elliptic & Parabolic Equations
Elliptic & Parabolic Equations

Author: Zhuoqun Wu

Publisher: World Scientific

Published: 2006

Total Pages: 428

ISBN-13: 9812700250

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This book provides an introduction to elliptic and parabolic equations. While there are numerous monographs focusing separately on each kind of equations, there are very few books treating these two kinds of equations in combination. This book presents the related basic theories and methods to enable readers to appreciate the commonalities between these two kinds of equations as well as contrast the similarities and differences between them.

Nonlinear Parabolic and Elliptic Equations
Nonlinear Parabolic and Elliptic Equations

Author: C.V. Pao

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 786

ISBN-13: 1461530342

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In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.

Numerical Solution of Elliptic and Parabolic Partial Differential Equations with CD-ROM
Numerical Solution of Elliptic and Parabolic Partial Differential Equations with CD-ROM

Author: John A. Trangenstein

Publisher: Cambridge University Press

Published: 2013-04-18

Total Pages: 657

ISBN-13: 0521877261

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For mathematicians and engineers interested in applying numerical methods to physical problems this book is ideal. Numerical ideas are connected to accompanying software, which is also available online. By seeing the complete description of the methods in both theory and implementation, students will more easily gain the knowledge needed to write their own application programs or develop new theory. The book contains careful development of the mathematical tools needed for analysis of the numerical methods, including elliptic regularity theory and approximation theory. Variational crimes, due to quadrature, coordinate mappings, domain approximation and boundary conditions, are analyzed. The claims are stated with full statement of the assumptions and conclusions, and use subscripted constants which can be traced back to the origination (particularly in the electronic version, which can be found on the accompanying CD-ROM).

Asymptotics of Elliptic and Parabolic PDEs
Asymptotics of Elliptic and Parabolic PDEs

Author: David Holcman

Publisher: Springer

Published: 2018-05-25

Total Pages: 456

ISBN-13: 3319768956

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This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.

Elliptic and Parabolic Problems
Elliptic and Parabolic Problems

Author: C Bandle

Publisher: CRC Press

Published: 2020-11-26

Total Pages: 272

ISBN-13: 1000115275

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This Research Note presents some recent advances in various important domains of partial differential equations and applied mathematics including equations and systems of elliptic and parabolic type and various applications in physics, mechanics and engineering. These topics are now part of various areas of science and have experienced tremendous development during the last decades. -------------------------------------