| Reviews |
| - 'This book is intended to introduce graduate students to the methods and results of nonlinear diffusion equations of porous medium type, as practised today. The present text, remarkable for generality and depth, is also notable for its author's concern, throughout, to keep the important issues about varieties clearly in the foreground ... [the book] succeeds admirably, in the reviewer's
opinion, in introducing its difficult subject at a level appropriate for preparing future workers in the field.' - Vicentiu Radulescu, Mathematical Reviews Issue 2007k
|
| Description | | - Provides a comprehensive and systematic guide to nonlinear diffusion equations
- End of chapter notes provide comments, historical notes and recommended reading
- Chapter-length list of references
| This text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of Physics, Chemistry, Biology, and Engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of
such equations is based on estimates and functional analysis.
Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity ("equations of porous medium type"), the aim of this text is to obtain sharp a priori estimates and decay rates for general classes of solutions in terms of estimates of particular problems. These estimates are
the building blocks in understanding the qualitative theory, and the decay rates pave the way to the fine study of asymptotics. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including time decay, smoothing, extinction in finite time, and delayed regularity. |
Readership: Graduates and researchers in mathematics, the physical sciences and engineering
| Contents |
Preface
Part I
1.
Preliminaries
2.
Smoothing effect and time decay. Data in L¹(R^n) or M(R^n)
3.
Smoothing effect and time decay from L^p or M^p
4.
Lower bounds, contractivity, error estimates and continuity
Part II
5.
Subcritical range of the FDE. Critical line. Extinction. Backward effect
6.
Improved analysis of the critical line. Delayed regularity
7.
Extinction rates and asymptotics for 0
8.
Logarithmic diffusion in 2-d and intermediate 1-d range
9.
Super-fast FDE
10.
Summary of main results for the PME/FDE
Part III
11.
Evolution equations of the p-Laplacian type
12.
Appendices
Bibliography
Index
|
| Authors, editors,
and contributors |
Juan Luis Vázquez, Universidad Autónoma de Madrid
|
The specification in this catalogue, including without
limitation price, format, extent, number of illustrations,
and month of publication, was as accurate as
possible at the time the catalogue was compiled.
Occasionally, due to the nature of some contractual restrictions, we
are unable to ship a specific product to a particular territory.
Jacket images are provisional and liable to change before publication.
|
VIEW BASKET
