Singularly Perturbed Evolution Equations With Applications To Kinetic Theory
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Singularly Perturbed Evolution Equations With Applications To Kinetic Theory
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Author : J. R. Mika
language : en
Publisher: World Scientific
Release Date : 1995
Singularly Perturbed Evolution Equations With Applications To Kinetic Theory written by J. R. Mika and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
In recent years there appeared a large number of papers as well as chapters in more general monographs devoted to evolution equations containing small (or large) parameters. In this book it is intended to gather the existing results as well as to introduce new ones on the field of initial value problems for singularly perturbed evolution equations of the resonance type. Such equations are of great interest in the applied sciences, particularly in the kinetic theory which is chosen as the main field of application for the asymptotic theory developed in the monograph.
Numerical Mathematics And Advanced Applications
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Author : Karl Kunisch
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-19
Numerical Mathematics And Advanced Applications written by Karl Kunisch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-19 with Mathematics categories.
The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of conferences held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. The ?rst ENUMATH conference was held in Paris (1995), and the series continued by the one in Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), and Santiago de Compostela (2005). This volume contains a selection of invited plenary lectures, papers presented in minisymposia, and contributed papers of ENUMATH 2007, held in Graz, Austria, September 10–14, 2007. We are happy that so many people have shown their interest in this conference. In addition to the ten invited presentations and the public lecture, we had more than 240 talks in nine minisymposia and ?fty four sessions of contributed talks, and about 316 participants from all over the world, specially from Europe. A total of 98 contributions appear in these proceedings. Topics include theoretical aspects of new numerical techniques and algorithms, as well as to applications in engineering and science. The book will be useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scienti?c computing and their applications. We would like to thank all the participants for the attendance and for their va- ablecontributionsanddiscussionsduringtheconference.Specialthanksgothe m- isymposium organizers, who made a large contribution to the conference, the chair persons, and all speakers.
Methods Of Small Parameter In Mathematical Biology
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Author : Jacek Banasiak
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-19
Methods Of Small Parameter In Mathematical Biology written by Jacek Banasiak and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-19 with Mathematics categories.
This monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant to the purpose at hand and preserves the salient features of the dynamics. Many ad hoc methods have been devised, and the aim of this book is to present a systematic way of deriving the so-called limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools the authors describe allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value. The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques. Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and graduate students in applied and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis.
Evolution Equations And Approximations
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Author : Kazufumi Ito
language : en
Publisher: World Scientific
Release Date : 2002-05-24
Evolution Equations And Approximations written by Kazufumi Ito and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-24 with Mathematics categories.
This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille–Yosida), nonlinear (Crandall–Liggett) and time-dependent (Crandall–Pazy) theorems. The implicit finite difference method of Euler is shown to generate a sequence convergent to the unique integral solution of evolution equations of the maximal monotone type. Moreover, the Chernoff theory provides a sufficient condition for consistent and stable time integration of time-dependent nonlinear equations. The Trotter–Kato theorem and the Lie–Trotter type product formula give a mathematical framework for the convergence analysis of numerical approximations of solutions to a general class of partial differential equations. This book contains examples demonstrating the applicability of the generation as well as the approximation theory. In addition, the Kobayashi–Oharu approach of locally quasi-dissipative operators is discussed for homogeneous as well as nonhomogeneous equations. Applications to the delay differential equations, Navier–Stokes equation and scalar conservation equation are given. Contents: Dissipative and Maximal Monotone OperatorsLinear SemigroupsAnalytic SemigroupsApproximation of C0-SemigroupsNonlinear Semigroups of ContractionsLocally Quasi-Dissipative Evolution EquationsThe Crandall–Pazy ClassVariational Formulations and Gelfand TriplesApplications to Concrete SystemsApproximation of Solutions for Evolution EquationsSemilinear Evolution EquationsAppendices:Some InequalitiesConvergence of Steklov MeansSome Technical Results Needed in Section 9.2 Readership: Researchers in the fields of analysis & differential equations and approximation theory. Keywords:Evolution Equations;Approximations;Euler;Trotter-Kato;Lie-Trotter;Quasi-Dissipative Operators;K and Y Kobayashi;S OharuReviews:“Ito and Kappel offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K and Y Kobayashi and S Oharu … their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses.”Book News, Inc.
Recent Developments In Evolution Equations
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Author : G F Roach
language : en
Publisher: CRC Press
Release Date : 1995-04-28
Recent Developments In Evolution Equations written by G F Roach and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-28 with Mathematics categories.
This book presents the majority of talks given at an International Converence held recently at the University of Strathclyde in Glasgow. The works presented focus on the analysis of mathematical models of systems evolving with time. The main topics are semigroups and related subjects connected with applications to partial differential equations of evolution type. Topics of particular interest include spectral and asymptotic properties of semigroups, B evolution scattering theory, and coagulation fragmentation phenomena.
Multiple Time Scale Dynamics
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Author : Christian Kuehn
language : en
Publisher: Springer
Release Date : 2015-02-25
Multiple Time Scale Dynamics written by Christian Kuehn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-25 with Mathematics categories.
This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Differential Equations Bifurcations And Chaos In Economics
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Author : Wei-Bin Zhang
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-07-18
Differential Equations Bifurcations And Chaos In Economics written by Wei-Bin Zhang and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-18 with Business & Economics categories.
Although the application of differential equations to economics is a vast and vibrant area, the subject has not been systematically studied; it is often treated as a subsidiary part of mathematical economics textbooks. This book aims to fill that void by providing a unique blend of the theory of differential equations and their exciting applications to dynamic economics. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been widely applied to economic analysis in recent years. It provides comprehensive coverage of the most important concepts and theorems in the theory of differential equations in a way that can be understood by any reader who has a basic knowledge of calculus and linear algebra. In addition to traditional applications of the theory to economic dynamics, the book includes many recent developments in different fields of economics.
Multigroup Equations For The Description Of The Particle Transport In Semiconductors
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Author : Martin Galler
language : en
Publisher: World Scientific
Release Date : 2005
Multigroup Equations For The Description Of The Particle Transport In Semiconductors written by Martin Galler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Technology & Engineering categories.
Deterministic simulation of the particle transport in semiconductor devices is an interesting alternative to the common Monte Carlo approach. In this book, a state-of-the-art technique called the multigroup approach is presented and applied to a variety of transport problems in bulk semiconductors and semiconductor devices. High-field effects as well as hot-phonon phenomena in polar semiconductors are studied in detail. The mathematical properties of the presented numerical method are studied, and the method is applied to simulating the transport of a two-dimensional electron gas formed at a semiconductor heterostructure. Concerning semiconductor device simulation, several diodes and transistors fabricated of silicon and gallium arsenide are investigated. For all of these simulations, the numerical techniques employed are discussed in detail. This unique study of the application of direct methods for semiconductor device simulation provides the interested reader with an indispensable reference on this growing research area.
Perturbations Of Positive Semigroups With Applications
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Author : Jacek Banasiak
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-02
Perturbations Of Positive Semigroups With Applications written by Jacek Banasiak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-02 with Mathematics categories.
This book deals mainly with modelling systems that change with time. The evolution equations that it describes can be found in a number of application areas, such as kinetics, fragmentation theory and mathematical biology. This will be the first self-contained account of the area.
Advanced Mathematical Computational Tools In Metrology Vii
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Author : P. Ciarlini
language : en
Publisher: World Scientific
Release Date : 2006
Advanced Mathematical Computational Tools In Metrology Vii written by P. Ciarlini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Computers categories.
This volume collects the refereed contributions based on the presentations made at the Seventh Workshop on Advanced Mathematical and Computational Tools in Metrology, a forum for metrologists, mathematicians and software engineers that will encourage a more effective synthesis of skills, capabilities and resources. The volume contains articles by world renowned metrologists and mathematicians involved in measurement science and, together with the six previous volumes in this series, constitutes an authoritative source of the mathematical, statistical and software tools necessary in modern metrology. Contents: Modeling Measurement Processes in Complex Systems with Partial Differential Equations: From Heat Conduction to the Heart (M Baer et al.); Mereotipological Approach for Measurement Software (E Benoit & R Dapoigny); Data Evaluation of Key Comparisons Involving Several Artefacts (M G Cox et al.); Box-Cox Transformations Versus Robust Control Charts in Statistical Process Control (M I Gomes & F O Figueiredo); Decision Making Using Sensor's Data Fusion and Kohonen Self Organizing Maps (P S Girao et al.); Generic System Design for Measurement Databases Applied to Calibrations in Vacuum Metrology, Bio-Signals and a Template System (H Gro et al.); Repeated Measurements: Evaluation of Their Uncertainty from the Viewpoints of Classical and Bayesian Statistics (I Lira & W Woger); Detection of Outliers in Interlaboratory Testing and Some Thoughts About Multivariate Precision (C Perruchet); On Appropriate Methods for the Validation of Metrological Software (D Richter et al.); Data Analysis-A Dialogue (D S Sivia); Validation of a Virtual Sensor for Monitoring Ambient Parameters (P Ciarlini et al.); Evaluation of Standard Uncertainties in Nested Structures (E Filipe); Linking GUM and ISO 5725 (A B Forbes); Monte Carlo Study on Logical and Statistical Correlation (B Siebert et al.); Some Problems Concerning the Estimate of the Uncertainty of the Degree of Equivalence in MRA Key Comparisons (F Pavese); Preparing for a European Research Area Network in Metrology: Where are We Now? (M Kuhne et al.); and other papers. Readership: Researchers, graduate students, academics and professionals in metrology.