Nonlinear Parabolic and Elliptic Equations

Nonlinear Parabolic and Elliptic Equations
Author: C.V. Pao
Publisher: Springer Science & Business Media
Total Pages: 814
Release: 1992
Genre: Mathematics
ISBN: 9780306443435

The recent development of reaction diffusion systems in biology, ecology and biochemistry, and the traditional importance of these systems in physics, heat-mass transfer, and engineering lead to extensive study in nonlinear parabolic and elliptical partial differential equations. This text provides an introduction to the subject as well as applicat.

Nonlinear Elliptic Equations of the Second Order

Nonlinear Elliptic Equations of the Second Order
Author: Qing Han
Publisher: American Mathematical Soc.
Total Pages: 378
Release: 2016-04-15
Genre: Mathematics
ISBN: 1470426072

Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler–Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge–Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and “elementary” proofs for results in important special cases. This book will serve as a valuable resource for graduate students or anyone interested in this subject.

Nonlinear Elliptic and Parabolic Equations of the Second Order

Nonlinear Elliptic and Parabolic Equations of the Second Order
Author: N.V. Krylov
Publisher: Springer
Total Pages: 0
Release: 2001-11-30
Genre: Mathematics
ISBN: 9781402003349

Approach your problems from the It isn't that they can't see the right end and begin with the solution. It is that they can't see answers. Then one day, perhaps the problem. you will find the final question. G.K. Chesterton. The Scandal of 'The Hermit Clad in Crane Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theor.etical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

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.
Total Pages: 178
Release: 1996
Genre: Mathematics
ISBN: 082180569X

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.

Elliptic and Parabolic Equations with Discontinuous Coefficients

Elliptic and Parabolic Equations with Discontinuous Coefficients
Author: Antonino Maugeri
Publisher: Wiley-VCH
Total Pages: 266
Release: 2000-12-13
Genre: Mathematics
ISBN:

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.

Nonlinear Elliptic Partial Differential Equations

Nonlinear Elliptic Partial Differential Equations
Author: Hervé Le Dret
Publisher: Springer
Total Pages: 259
Release: 2018-05-25
Genre: Mathematics
ISBN: 3319783904

This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.

Nonlinear Parabolic and Elliptic Equations

Nonlinear Parabolic and Elliptic Equations
Author: C.V. Pao
Publisher: Springer Science & Business Media
Total Pages: 786
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461530342

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.

Elliptic & Parabolic Equations

Elliptic & Parabolic Equations
Author: Zhuoqun Wu
Publisher: World Scientific
Total Pages: 428
Release: 2006
Genre: Mathematics
ISBN: 9812700250

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.

Partial Differential Equations of Parabolic Type

Partial Differential Equations of Parabolic Type
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.