Parabolic Problems PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Parabolic Problems PDF full book. Access full book title Parabolic Problems.
Author | : Pavol Quittner |
Publisher | : Springer Science & Business Media |
Total Pages | : 593 |
Release | : 2007-12-16 |
Genre | : Mathematics |
ISBN | : 3764384425 |
Download Superlinear Parabolic Problems Book in PDF, ePub and Kindle
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 book is self-contained and up-to-date, taking special care on the didactical preparation of the material. It is devoted to problems that are intensively studied but have not been treated thus far in depth in the book literature.
Author | : Herbert Amann |
Publisher | : Birkhäuser |
Total Pages | : 366 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034892217 |
Download Linear and Quasilinear Parabolic Problems Book in PDF, ePub and Kindle
In this treatise we present the semigroup approach to quasilinear evolution equa of parabolic type that has been developed over the last ten years, approxi tions mately. It emphasizes the dynamic viewpoint and is sufficiently general and flexible to encompass a great variety of concrete systems of partial differential equations occurring in science, some of those being of rather 'nonstandard' type. In partic ular, to date it is the only general method that applies to noncoercive systems. Although we are interested in nonlinear problems, our method is based on the theory of linear holomorphic semigroups. This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille Yosida theorem: the Crandall-Liggett theorem. The latter theory is well-known and well-documented in the literature. Even though it is a powerful technique having found many applications, it is limited in its scope by the fact that, in concrete applications, it is closely tied to the maximum principle. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle. For these reasons we do not include that theory.
Author | : Vidar Thomee |
Publisher | : Springer Science & Business Media |
Total Pages | : 310 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662033593 |
Download Galerkin Finite Element Methods for Parabolic Problems Book in PDF, ePub and Kindle
My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.
Author | : Samuil D. Eidelman |
Publisher | : Birkhäuser |
Total Pages | : 307 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034887671 |
Download Parabolic Boundary Value Problems Book in PDF, ePub and Kindle
The present monograph is devoted to the theory of general parabolic boundary value problems. The vastness of this theory forced us to take difficult decisions in selecting the results to be presented and in determining the degree of detail needed to describe their proofs. In the first chapter we define the basic notions at the origin of the theory of parabolic boundary value problems and give various examples of illustrative and descriptive character. The main part of the monograph (Chapters II to V) is devoted to a the detailed and systematic exposition of the L -theory of parabolic 2 boundary value problems with smooth coefficients in Hilbert spaces of smooth functions and distributions of arbitrary finite order and with some natural appli cations of the theory. Wishing to make the monograph more informative, we included in Chapter VI a survey of results in the theory of the Cauchy problem and boundary value problems in the traditional spaces of smooth functions. We give no proofs; rather, we attempt to compare different results and techniques. Special attention is paid to a detailed analysis of examples illustrating and complementing the results for mulated. The chapter is written in such a way that the reader interested only in the results of the classical theory of the Cauchy problem and boundary value problems may concentrate on it alone, skipping the previous chapters.
Author | : Emmanuele DiBenedetto |
Publisher | : Springer Science & Business Media |
Total Pages | : 402 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461208955 |
Download Degenerate Parabolic Equations Book in PDF, ePub and Kindle
Evolved from the author's lectures at the University of Bonn's Institut für angewandte Mathematik, this book reviews recent progress toward understanding of the local structure of solutions of degenerate and singular parabolic partial differential equations.
Author | : Herbert Amann |
Publisher | : Springer |
Total Pages | : 462 |
Release | : 2019-04-16 |
Genre | : Mathematics |
ISBN | : 3030117634 |
Download Linear and Quasilinear Parabolic Problems Book in PDF, ePub and Kindle
This volume discusses an in-depth theory of function spaces in an Euclidean setting, including several new features, not previously covered in the literature. In particular, it develops a unified theory of anisotropic Besov and Bessel potential spaces on Euclidean corners, with infinite-dimensional Banach spaces as targets. It especially highlights the most important subclasses of Besov spaces, namely Slobodeckii and Hölder spaces. In this case, no restrictions are imposed on the target spaces, except for reflexivity assumptions in duality results. In this general setting, the author proves sharp embedding, interpolation, and trace theorems, point-wise multiplier results, as well as Gagliardo-Nirenberg estimates and generalizations of Aubin-Lions compactness theorems. The results presented pave the way for new applications in situations where infinite-dimensional target spaces are relevant – in the realm of stochastic differential equations, for example.
Author | : Tomasz W. Dłotko |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 217 |
Release | : 2020-05-05 |
Genre | : Mathematics |
ISBN | : 311059868X |
Download Critical Parabolic-Type Problems Book in PDF, ePub and Kindle
This self-contained book covers the theory of semilinear equations with sectorial operator going back to the studies of Yosida, Henry, and Pazy, which are deeply extended nowadays. The treatment emphasizes existence-uniqueness theory as a topic of functional analysis and examines abstract evolutionary equations, with applications to the Navier-Stokes system, the quasi-geostrophic equation, and fractional reaction-diffusion equations.
Author | : David Angell |
Publisher | : CRC Press |
Total Pages | : 296 |
Release | : 2024-06-27 |
Genre | : Mathematics |
ISBN | : 1040041647 |
Download Parabolic Problems Book in PDF, ePub and Kindle
Parabola is a mathematics magazine published by UNSW, Sydney. Among other things, each issue of Parabola has contained a collection of puzzles/problems, on various mathematical topics and at a suitable level for younger (but mathematically sophisticated) readers. Parabolic Problems: 60 Years of Mathematical Puzzles in Parabola collects the very best of almost 1800 problems and puzzles into a single volume. Many of the problems have been re-mastered, and new illustrations have been added. Topics covered range across geometry, number theory, combinatorics, logic, and algebra. Solutions are provided to all problems, and a chapter has been included detailing some frequently useful problem-solving techniques, making this a fabulous resource for education and, most importantly, fun! Features Hundreds of diverting and mathematically interesting problems and puzzles. Accessible for anyone with a high school-level mathematics education. Wonderful resource for teachers and students of mathematics from high school to undergraduate level, and beyond.
Author | : Nikolaĭ Vladimirovich Krylov |
Publisher | : American Mathematical Soc. |
Total Pages | : 178 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 082180569X |
Download Lectures on Elliptic and Parabolic Equations in Holder Spaces Book in PDF, ePub and Kindle
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.
Author | : Alessandra Lunardi |
Publisher | : Springer Science & Business Media |
Total Pages | : 437 |
Release | : 2012-12-13 |
Genre | : Mathematics |
ISBN | : 3034805578 |
Download Analytic Semigroups and Optimal Regularity in Parabolic Problems Book in PDF, ePub and Kindle
The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques. - - - This very interesting book provides a systematic treatment of the basic theory of analytic semigroups and abstract parabolic equations in general Banach spaces, and how this theory may be used in the study of parabolic partial differential equations; it takes into account the developments of the theory during the last fifteen years. (...) For instance, optimal regularity results are a typical feature of abstract parabolic equations; they are comprehensively studied in this book, and yield new and old regularity results for parabolic partial differential equations and systems. (Mathematical Reviews) Motivated by applications to fully nonlinear problems the approach is focused on classical solutions with continuous or Hölder continuous derivatives. (Zentralblatt MATH)