Matched Asymptotic Expansions In Reaction Diffusion Theory
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Author | : J.A. Leach |
Publisher | : Springer Science & Business Media |
Total Pages | : 289 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 0857293966 |
This volume contains a wealth of results and methodologies applicable to a wide range of problems arising in reaction-diffusion theory. It can be viewed both as a handbook, and as a detailed description of the methodology. The authors present new methods based on matched asymptotic expansions.
Author | : J. A. Leach |
Publisher | : |
Total Pages | : 304 |
Release | : 2003-11-01 |
Genre | : |
ISBN | : 9780857293978 |
Author | : John Leach |
Publisher | : Springer |
Total Pages | : 290 |
Release | : 2012-10-23 |
Genre | : Mathematics |
ISBN | : 9781447110545 |
This volume contains a wealth of results and methodologies applicable to a wide range of problems arising in reaction-diffusion theory. It can be viewed both as a handbook, and as a detailed description of the methodology. The authors present new methods based on matched asymptotic expansions.
Author | : |
Publisher | : Elsevier |
Total Pages | : 153 |
Release | : 2011-08-26 |
Genre | : Mathematics |
ISBN | : 0080871178 |
Matched Asymptotic Expansions and Singular Perturbations
Author | : Augustin Fruchard |
Publisher | : Springer |
Total Pages | : 169 |
Release | : 2012-12-15 |
Genre | : Mathematics |
ISBN | : 3642340350 |
The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance problem is solved.
Author | : P.A. Lagerstrom |
Publisher | : Springer Science & Business Media |
Total Pages | : 263 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475719906 |
Content and Aims of this Book Earlier drafts of the manuscript of this book (James A. Boa was then coau thor) contained discussions of many methods and examples of singular perturba tion problems. The ambitious plans of covering a large number of topics were later abandoned in favor of the present goal: a thorough discussion of selected ideas and techniques used in the method of matched asymptotic expansions. Thus many problems and methods are not covered here: the method of av eraging and the related method of multiple scales are mentioned mainly to give reasons why they are not discussed further. Examples which required too sophis ticated and involved calculations, or advanced knowledge of a special field, are not treated; for instance, to the author's regret some very interesting applications to fluid mechanics had to be omitted for this reason. Artificial mathematical examples introduced to show some exotic or unexpected behavior are omitted, except when they are analytically simple and are needed to illustrate mathematical phenomena important for realistic problems. Problems of numerical analysis are not discussed.
Author | : J. C. Meyer |
Publisher | : Cambridge University Press |
Total Pages | : 177 |
Release | : 2015-10-22 |
Genre | : Mathematics |
ISBN | : 1107477395 |
A monograph containing significant new developments in the theory of reaction-diffusion systems, particularly those arising in chemistry and life sciences.
Author | : Wladyslaw Narkiewicz |
Publisher | : Springer Science & Business Media |
Total Pages | : 712 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662070014 |
This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.
Author | : Michel Talagrand |
Publisher | : Springer Science & Business Media |
Total Pages | : 240 |
Release | : 2005-03-17 |
Genre | : Mathematics |
ISBN | : 9783540245186 |
The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After contributions by R. Dudley and X. Fernique, it was solved by the author. This book provides an overview of "generic chaining", a completely natural variation on the ideas of Kolmogorov. It takes the reader from the first principles to the edge of current knowledge and to the open problems that remain in this domain.
Author | : R. J. Adler |
Publisher | : Springer Science & Business Media |
Total Pages | : 455 |
Release | : 2009-01-29 |
Genre | : Mathematics |
ISBN | : 0387481168 |
This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.