Asymptotic Analysis For Periodic Structures
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Author | : Alain Bensoussan |
Publisher | : American Mathematical Soc. |
Total Pages | : 410 |
Release | : 2011-10-26 |
Genre | : Mathematics |
ISBN | : 0821853244 |
This is a reprinting of a book originally published in 1978. At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic methods. At the time the book was written the use of asymptotic expansions with multiple scales was new, especially their use as a theoretical tool, combined with energy methods and the construction of test functions for analysis with weak convergence methods. Before this book, multiple scale methods were primarily used for non-linear oscillation problems in the applied mathematics community, not for analyzing spatial oscillations as in homogenization. In the current printing a number of minor corrections have been made, and the bibliography was significantly expanded to include some of the most important recent references. This book gives systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate. The book continues to be interesting and useful to readers of different backgrounds, both from pure and applied mathematics, because of its informal style of introducing the multiple scale methodology and the detailed proofs.
Author | : Alain Bensoussan |
Publisher | : North Holland |
Total Pages | : 700 |
Release | : 1978 |
Genre | : Asymptotic expansions |
ISBN | : 9780444851727 |
Author | : Alain Bensoussan |
Publisher | : |
Total Pages | : |
Release | : 1978 |
Genre | : |
ISBN | : |
Author | : F. Verhulst |
Publisher | : Springer |
Total Pages | : 503 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540396128 |
Author | : L.I. Manevitch |
Publisher | : Springer Science & Business Media |
Total Pages | : 276 |
Release | : 2013-11-11 |
Genre | : Technology & Engineering |
ISBN | : 3540445714 |
Rigorous presentation of Mathematical Homogenization Theory is the subject of numerous publications. This book, however, is intended to fill the gap in the analytical and numerical performance of the corresponding asymptotic analysis of the static and dynamic behaviors of heterogenous systems. Numerous concrete applications to composite media, heterogeneous plates and shells are considered. A lot of details, numerical results for cell problem solutions, calculations of high-order terms of asymptotic expansions, boundary layer analysis etc., are included.
Author | : Mikhail V. Fedoryuk |
Publisher | : Springer Science & Business Media |
Total Pages | : 370 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642580165 |
In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.
Author | : Philippe G. Ciarlet |
Publisher | : Springer |
Total Pages | : 232 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : |
Author | : Vicente Romero-Garcia |
Publisher | : John Wiley & Sons |
Total Pages | : 320 |
Release | : 2019-08-08 |
Genre | : Technology & Engineering |
ISBN | : 1119649161 |
In the last few decades, metamaterials have revolutionized the ways in which waves are controlled, and applied in physics and practical situations. The extraordinary properties of metamaterials, such as their locally resonant structure with deep subwavelength band gaps and their ranges of frequency where propagation is impossible, have opened the way to a host of applications that were previously unavailable. Acoustic metamaterials have been able to replace traditional treatments in several sectors, due to their better performance in targeted and tunable frequency ranges with strongly reduced dimensions. This is a training book composed of nine chapters written by experts in the field, giving a broad overview of acoustic metamaterials and their uses. The book is divided into three parts, covering the state-of-the-art, the fundamentals and the real-life applications of acoustic metamaterials.
Author | : Hans G. Kaper |
Publisher | : CRC Press |
Total Pages | : 283 |
Release | : 1991-02-25 |
Genre | : Mathematics |
ISBN | : 1482277069 |
Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
Author | : Vladimir Kozlov |
Publisher | : Oxford University Press, USA |
Total Pages | : 308 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 9780198514954 |
This book outlines a powerful new method in analysis which has already been instrumental in solving complicated partial differential equations arising in various areas of engineering. It is suitable for those working with partial differential equations and their applications, and an undergraduate knowledge of PDE's and functional analysis is assumed.