Propagation Phenomena In Reaction Advection Diffusion Equations

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Nonlinear PDE’s in Condensed Matter and Reactive Flows

Author : Henri Berestycki
Publisher : Springer Science & Business Media
ISBN 13 : 9781402009723
Total Pages : 554 pages
Book Rating : 4.0/5 (97 download)

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Book Synopsis Nonlinear PDE’s in Condensed Matter and Reactive Flows by : Henri Berestycki

Download or read book Nonlinear PDE’s in Condensed Matter and Reactive Flows written by Henri Berestycki and published by Springer Science & Business Media. This book was released on 2002-11-30 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear partial differential equations abound in modern physics. The problems arising in these fields lead to fascinating questions and, at the same time, progress in understanding the mathematical structures is of great importance to the models. Nevertheless, activity in one of the approaches is not always sufficiently in touch with developments in the other field. The book presents the joint efforts of mathematicians and physicists involved in modelling reactive flows, in particular superconductivity and superfluidity. Certain contributions are fundamental to an understanding of such cutting-edge research topics as rotating Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak turbulence equations, and the propagation of fronts in heterogeneous media.

Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations

Author : Willem Hundsdorfer
Publisher : Springer Science & Business Media
ISBN 13 : 3662090171
Total Pages : 479 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations by : Willem Hundsdorfer

Download or read book Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations written by Willem Hundsdorfer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unique book on Reaction-Advection-Diffusion problems

Nonlinear PDE’s in Condensed Matter and Reactive Flows

Author : Henri Berestycki
Publisher : Springer Science & Business Media
ISBN 13 : 9401003076
Total Pages : 525 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Nonlinear PDE’s in Condensed Matter and Reactive Flows by : Henri Berestycki

Download or read book Nonlinear PDE’s in Condensed Matter and Reactive Flows written by Henri Berestycki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear partial differential equations abound in modern physics. The problems arising in these fields lead to fascinating questions and, at the same time, progress in understanding the mathematical structures is of great importance to the models. Nevertheless, activity in one of the approaches is not always sufficiently in touch with developments in the other field. The book presents the joint efforts of mathematicians and physicists involved in modelling reactive flows, in particular superconductivity and superfluidity. Certain contributions are fundamental to an understanding of such cutting-edge research topics as rotating Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak turbulence equations, and the propagation of fronts in heterogeneous media.

Computational Algorithms for Shallow Water Equations

Author : Eleuterio F. Toro
Publisher : Springer Nature
ISBN 13 : 3031613953
Total Pages : 413 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Computational Algorithms for Shallow Water Equations by : Eleuterio F. Toro

Download or read book Computational Algorithms for Shallow Water Equations written by Eleuterio F. Toro and published by Springer Nature. This book was released on with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Role of Advection in a Two-Species Competition Model: A Bifurcation Approach

Author : Isabel Averill
Publisher : American Mathematical Soc.
ISBN 13 : 1470422026
Total Pages : 118 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Role of Advection in a Two-Species Competition Model: A Bifurcation Approach by : Isabel Averill

Download or read book The Role of Advection in a Two-Species Competition Model: A Bifurcation Approach written by Isabel Averill and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The effects of weak and strong advection on the dynamics of reaction-diffusion models have long been studied. In contrast, the role of intermediate advection remains poorly understood. For example, concentration phenomena can occur when advection is strong, providing a mechanism for the coexistence of multiple populations, in contrast with the situation of weak advection where coexistence may not be possible. The transition of the dynamics from weak to strong advection is generally difficult to determine. In this work the authors consider a mathematical model of two competing populations in a spatially varying but temporally constant environment, where both species have the same population dynamics but different dispersal strategies: one species adopts random dispersal, while the dispersal strategy for the other species is a combination of random dispersal and advection upward along the resource gradient. For any given diffusion rates the authors consider the bifurcation diagram of positive steady states by using the advection rate as the bifurcation parameter. This approach enables the authors to capture the change of dynamics from weak advection to strong advection. The authors determine three different types of bifurcation diagrams, depending on the difference of diffusion rates. Some exact multiplicity results about bifurcation points are also presented. The authors' results can unify some previous work and, as a case study about the role of advection, also contribute to the understanding of intermediate (relative to diffusion) advection in reaction-diffusion models.

An Introduction to Fronts in Random Media

Author : Jack Xin
Publisher : Springer Science & Business Media
ISBN 13 : 0387876839
Total Pages : 165 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis An Introduction to Fronts in Random Media by : Jack Xin

Download or read book An Introduction to Fronts in Random Media written by Jack Xin and published by Springer Science & Business Media. This book was released on 2009-06-17 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to give a user friendly tutorial of an interdisciplinary research topic (fronts or interfaces in random media) to senior undergraduates and beginning grad uate students with basic knowledge of partial differential equations (PDE) and prob ability. The approach taken is semiformal, using elementary methods to introduce ideas and motivate results as much as possible, then outlining how to pursue rigor ous theorems, with details to be found in the references section. Since the topic concerns both differential equations and probability, and proba bility is traditionally a quite technical subject with a heavy measure theoretic com ponent, the book strives to develop a simplistic approach so that students can grasp the essentials of fronts and random media and their applications in a self contained tutorial. The book introduces three fundamental PDEs (the Burgers equation, Hamilton– Jacobi equations, and reaction–diffusion equations), analysis of their formulas and front solutions, and related stochastic processes. It builds up tools gradually, so that students are brought to the frontiers of research at a steady pace. A moderate number of exercises are provided to consolidate the concepts and ideas. The main methods are representation formulas of solutions, Laplace meth ods, homogenization, ergodic theory, central limit theorems, large deviation princi ples, variational principles, maximum principles, and Harnack inequalities, among others. These methods are normally covered in separate books on either differential equations or probability. It is my hope that this tutorial will help to illustrate how to combine these tools in solving concrete problems.

Perspectives in Nonlinear Partial Differential Equations

Author : Henri Berestycki
Publisher : American Mathematical Soc.
ISBN 13 : 0821841904
Total Pages : 522 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Perspectives in Nonlinear Partial Differential Equations by : Henri Berestycki

Download or read book Perspectives in Nonlinear Partial Differential Equations written by Henri Berestycki and published by American Mathematical Soc.. This book was released on 2007 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: In celebration of Haim Brezis's 60th birthday, a conference was held at the Ecole Polytechnique in Paris, with a program testifying to Brezis's wide-ranging influence on nonlinear analysis and partial differential equations. The articles in this volume are primarily from that conference. They present a rare view of the state of the art of many aspects of nonlinear PDEs, as well as describe new directions that are being opened up in this field. The articles, written by mathematicians at the center of current developments, provide somewhat more personal views of the important developments and challenges.

Non-Newtonian Fluid Mechanics and Complex Flows

Author : Angiolo Farina
Publisher : Springer
ISBN 13 : 3319747967
Total Pages : 308 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Non-Newtonian Fluid Mechanics and Complex Flows by : Angiolo Farina

Download or read book Non-Newtonian Fluid Mechanics and Complex Flows written by Angiolo Farina and published by Springer. This book was released on 2018-06-25 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a series of challenging mathematical problems which arise in the modeling of Non-Newtonian fluid dynamics. It focuses in particular on the mathematical and physical modeling of a variety of contemporary problems, and provides some results. The flow properties of Non-Newtonian fluids differ in many ways from those of Newtonian fluids. Many biological fluids (blood, for instance) exhibit a non-Newtonian behavior, as do many naturally occurring or technologically relevant fluids such as molten polymers, oil, mud, lava, salt solutions, paint, and so on. The term "complex flows" usually refers to those fluids presenting an "internal structure" (fluid mixtures, solutions, multiphase flows, and so on). Modern research on complex flows has increased considerably in recent years due to the many biological and industrial applications.

The Mathematics of Diffusion

Author : John Crank
Publisher : Oxford University Press
ISBN 13 : 9780198534112
Total Pages : 428 pages
Book Rating : 4.5/5 (341 download)

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Book Synopsis The Mathematics of Diffusion by : John Crank

Download or read book The Mathematics of Diffusion written by John Crank and published by Oxford University Press. This book was released on 1979 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.

Equadiff 2003 - Proceedings Of The International Conference On Differential Equations

Author : Freddy Dumortier
Publisher : World Scientific
ISBN 13 : 9814480916
Total Pages : 1180 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Equadiff 2003 - Proceedings Of The International Conference On Differential Equations by : Freddy Dumortier

Download or read book Equadiff 2003 - Proceedings Of The International Conference On Differential Equations written by Freddy Dumortier and published by World Scientific. This book was released on 2005-02-23 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume contains the state of the art on ODE's and PDE's of different nature, functional differential equations, delay equations, and others, mostly from the dynamical systems point of view.A broad range of topics are treated through contributions by leading experts of their fields, presenting the most recent developments. A large variety of techniques are being used, stressing geometric, topological, ergodic and numerical aspects.The scope of the book is wide, ranging from pure mathematics to various applied fields. Examples of the latter are provided by subjects from earth and life sciences, classical mechanics and quantum-mechanics, among others.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences

Dynamical Systems in Population Biology

Author : Xiao-Qiang Zhao
Publisher : Springer Science & Business Media
ISBN 13 : 0387217614
Total Pages : 285 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Dynamical Systems in Population Biology by : Xiao-Qiang Zhao

Download or read book Dynamical Systems in Population Biology written by Xiao-Qiang Zhao and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Population dynamics is an important subject in mathematical biology. A cen tral problem is to study the long-term behavior of modeling systems. Most of these systems are governed by various evolutionary equations such as difference, ordinary, functional, and partial differential equations (see, e. g. , [165, 142, 218, 119, 55]). As we know, interactive populations often live in a fluctuating environment. For example, physical environmental conditions such as temperature and humidity and the availability of food, water, and other resources usually vary in time with seasonal or daily variations. Therefore, more realistic models should be nonautonomous systems. In particular, if the data in a model are periodic functions of time with commensurate period, a periodic system arises; if these periodic functions have different (minimal) periods, we get an almost periodic system. The existing reference books, from the dynamical systems point of view, mainly focus on autonomous biological systems. The book of Hess [106J is an excellent reference for periodic parabolic boundary value problems with applications to population dynamics. Since the publication of this book there have been extensive investigations on periodic, asymptotically periodic, almost periodic, and even general nonautonomous biological systems, which in turn have motivated further development of the theory of dynamical systems. In order to explain the dynamical systems approach to periodic population problems, let us consider, as an illustration, two species periodic competitive systems dUI dt = !I(t,Ul,U2), (0.

The Kolmogorov Legacy in Physics

Author : Angelo Vulpiani
Publisher : Springer
ISBN 13 : 3540396683
Total Pages : 258 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis The Kolmogorov Legacy in Physics by : Angelo Vulpiani

Download or read book The Kolmogorov Legacy in Physics written by Angelo Vulpiani and published by Springer. This book was released on 2003-12-08 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume, published at the occasion of his 100th birthday anniversary, is a collection of articles that reviews the impact of Kolomogorov's work in the physical sciences and provides an introduction to the modern developments that have been triggered in this way to encompass recent applications in biology, chemistry, information sciences and finance.

Author :
Publisher : Springer Nature
ISBN 13 : 3031743792
Total Pages : 494 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis by :

Download or read book written by and published by Springer Nature. This book was released on with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Diffusion Equations

Author : Zhuoqun Wu
Publisher : World Scientific
ISBN 13 : 9810247184
Total Pages : 521 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Nonlinear Diffusion Equations by : Zhuoqun Wu

Download or read book Nonlinear Diffusion Equations written by Zhuoqun Wu and published by World Scientific. This book was released on 2001 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations.This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon.

Reaction-Diffusion Equations and Propagation Phenomena

Author : Henri Berestycki
Publisher : Springer Verlag
ISBN 13 : 9780387341583
Total Pages : 410 pages
Book Rating : 4.3/5 (415 download)

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Book Synopsis Reaction-Diffusion Equations and Propagation Phenomena by : Henri Berestycki

Download or read book Reaction-Diffusion Equations and Propagation Phenomena written by Henri Berestycki and published by Springer Verlag. This book was released on 2007-01-01 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is about reaction-diffusion equations in unbounded domains with a special emphasis on traveling waves and their generalizations as well as on different notions of propagation. It includes a general presentation of all the classical results in this area. Even for some well known results, in some cases, original proofs are included which are simpler and more elegant than the known ones. The book gives a fairly comprehensive and coherent account of the recent developments and current research in this active area. It also contains some of the basic results about elliptic and parabolic partial differential equations and a chapter on the different versions of the maximum principles. Thus, it also serves as an introduction to these topics. Each chapter is made as much autonomous as possible. Each one has a specific introduction as well as brief mentions of extensions or of related subjects. Some outstanding open problems are mentioned along the way. Each introduction states the goals of the chapter, some of its main results, the framework and indicates how the chapter is organized. The book is addressed to researchers and graduate students in mathematics, in particular in analysis, partial differential equations and applied mathematics. It will be of interest as well to researchers and graduate students concerned by mathematical modeling in physics and in biology. It is planed to be a reference book of lasting value with all the important results on a topic which is commonly used in these fields.

Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems

Author : Werner Ebeling
Publisher : World Scientific
ISBN 13 : 9810213824
Total Pages : 344 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems by : Werner Ebeling

Download or read book Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems written by Werner Ebeling and published by World Scientific. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents both the fundamentals and the major research topics in statistical physics of systems out of equilibrium. It summarizes different approaches to describe such systems on the thermodynamic and stochastic levels, and discusses a variety of areas including reactions, anomalous kinetics, and the behavior of self-propelling particles.

Finite Difference Computing with PDEs

Author : Hans Petter Langtangen
Publisher : Springer
ISBN 13 : 3319554565
Total Pages : 522 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Finite Difference Computing with PDEs by : Hans Petter Langtangen

Download or read book Finite Difference Computing with PDEs written by Hans Petter Langtangen and published by Springer. This book was released on 2017-06-21 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.