Large Time Behavior Of Solutions Of Linear Dispersive Equations
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| Author | : Daniel B. Dix |
| Publisher | : Springer |
| Total Pages | : 217 |
| Release | : 2006-11-13 |
| Genre | : Mathematics |
| ISBN | : 3540695451 |
This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension. Complete matched and uniformly-valid asymptotic expansions are obtained and sharp error estimates are proved. Using the method of steepest descent much new information on the regularity and spatial asymptotics of the solutions are also obtained. Applications to nonlinear dispersive equations are discussed. This monograph is intended for researchers and graduate students of partial differential equations. Familiarity with basic asymptotic, complex and Fourier analysis is assumed.
| Author | : A.S. Fokas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 563 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642580459 |
In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This is the first book to present a comprehensive overview of these developments. Numbered among the authors are many of the most prominent researchers in the field.
| Author | : |
| Publisher | : World Scientific |
| Total Pages | : 814 |
| Release | : 2011 |
| Genre | : |
| ISBN | : 9814324353 |
| Author | : Jaime Angulo Pava |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 272 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 0821848976 |
This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied include Korteweg-de Vries, Benjamin-Ono, and Schrodinger equations. Many special Jacobian elliptic functions play a role in these examples. The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena.
| Author | : V.D. Milman |
| Publisher | : Springer |
| Total Pages | : 296 |
| Release | : 2007-05-09 |
| Genre | : Mathematics |
| ISBN | : 354045392X |
This volume of original research papers from the Israeli GAFA seminar during the years 1996-2000 not only reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the recent new trends in Banach Space Theory and related topics. These include the tighter connection with convexity and the resulting added emphasis on convex bodies that are not necessarily centrally symmetric, and the treatment of bodies which have only very weak convex-like structure. Another topic represented here is the use of new probabilistic tools; in particular transportation of measure methods and new inequalities emerging from Poincaré-like inequalities.
| Author | : Andrea Braides |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 176 |
| Release | : 1998-09-17 |
| Genre | : Mathematics |
| ISBN | : 9783540647713 |
Functionals involving both volume and surface energies have a number of applications ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations, finite-difference or non-local energies, etc.) The purpose of this book is to present a global approach to these approximations using the theory of gamma-convergence and of special functions of bounded variation. The book is directed to PhD students and researchers in calculus of variations, interested in approximation problems with possible applications.
| Author | : Yahiko Kambayashi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 672 |
| Release | : 2004-08-18 |
| Genre | : Computers |
| ISBN | : 9783540229377 |
This book constitutes the refereed proceedings of the 6th International Conference on Data Warehousing and Knowledge Discovery, DaWaK 2004, held in Zaragoza, Spain, in September 2004. The 40 revised full papers presented were carefully reviewed and selected from over 100 submissions. The papers are organized in topical sections on data warehouse design; knowledge discovery framework and XML data mining, data cubes and queries; multidimensional schema and data aggregation; inductive databases and temporal rules; industrial applications; data clustering; data visualization and exploration; data classification, extraction, and interpretation; data semantics, association rule mining; event sequence mining; and pattern mining.
| Author | : M.S. Espedal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 236 |
| Release | : 2000-12-12 |
| Genre | : Science |
| ISBN | : 9783540678687 |
This book is devoted to the presentation of some flow problems in porous media having relevant industrial applications. The main topics covered are: the manufacturing of composite materials, the espresso coffee brewing process, the filtration of liquids through diapers, various questions about flow problems in oil reservoirs and the theory of homogenization. The aim is to show that filtration problems arising in very practical industrial context exhibit interesting and highly nontrivial mathematical aspects. Thus the style of the book is mathematically rigorous, but specifically oriented towards applications, so that it is intended for both applied mathematicians and researchers in various areas of technological interest. The reader is required to have a good knowledge of the classical theory of PDE and basic functional analysis.
| Author | : James H. Bramble |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 184 |
| Release | : 2003-10-22 |
| Genre | : Mathematics |
| ISBN | : 9783540200994 |
This volume aims to disseminate a number of new ideas that have emerged in the last few years in the field of numerical simulation, all bearing the common denominator of the "multiscale" or "multilevel" paradigm. This covers the presence of multiple relevant "scales" in a physical phenomenon; the detection and representation of "structures", localized in space or in frequency, in the solution of a mathematical model; the decomposition of a function into "details" that can be organized and accessed in decreasing order of importance; and the iterative solution of systems of linear algebraic equations using "multilevel" decompositions of finite dimensional spaces.
| Author | : Xingzhi Zhan |
| Publisher | : Springer |
| Total Pages | : 127 |
| Release | : 2004-10-19 |
| Genre | : Mathematics |
| ISBN | : 3540454217 |
The main purpose of this monograph is to report on recent developments in the field of matrix inequalities, with emphasis on useful techniques and ingenious ideas. Among other results this book contains the affirmative solutions of eight conjectures. Many theorems unify or sharpen previous inequalities. The author's aim is to streamline the ideas in the literature. The book can be read by research workers, graduate students and advanced undergraduates.
