Reaction Diffusion Equations
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Shock Waves And Reaction Diffusion Equations
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Author : Joel Smoller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Shock Waves And Reaction Diffusion Equations written by Joel Smoller 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 2012-12-06 with Mathematics categories.
For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con structing travelling waves for systems of nonlinear equations. The final sec tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica ble to many interesting reaction-diffusion systems.
Reaction Diffusion Equations And Their Applications To Biology
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Author : N. F. Britton
language : en
Publisher:
Release Date : 1986
Reaction Diffusion Equations And Their Applications To Biology written by N. F. Britton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Science categories.
Although the book is largely self-contained, some knowledge of the mathematics of differential equations is necessary. Thus the book is intended for mathematicians who are interested in the application of their subject to the biological sciences and for biologists with some mathematical training. It is also suitable for postgraduate mathematics students and for undergraduate mathematicians taking a course in mathematical biology. Increasing use of mathematics in developmental biology, ecology, physiology, and many other areas in the biological sciences has produced a need for a complete, mathematical reference for laboratory practice. In this volume, biological scientists will find a rich resource of interesting applications and illustrations of various mathematical techniques that can be used to analyze reaction-diffusion systems. Concepts covered here include:**systems of ordinary differential equations**conservative systems**the scalar reaction-diffusion equation**analytic techniques for systems of parabolic partial differential equations**bifurcation theory**asymptotic methods for oscillatory systems**singular perturbations**macromolecular carriers -- asymptotic techniques.
Reaction Diffusion Equations
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Author : K. J. Brown
language : en
Publisher: Oxford Science Publications
Release Date : 1990
Reaction Diffusion Equations written by K. J. Brown and has been published by Oxford Science Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
Reaction-diffusion equations form a class of differential equations which in recent years have seen great steps forward both in the understanding of their analytical structure and in their application to a wide variety of scientific phenomena. This volume comprises a collection of articles onthe theme of the theory and applications of reaction-diffusion equations. All the contributors are experts in their respective fields and together the articles will provide a coherent perspective to the current state of research in this area.Some of the articles survey particular applications such as in combustion theory, electrochemistry, and problems arising in the biological sciences such as cellular neurobiology and population dynamics. Other articles concentrate on the analytic behaviour of reatcion-diffusion equations such asblow-up, the formation of patterns, travelling wave solutions, and the Conley index.
Patterns And Waves
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Author : Peter Grindrod
language : en
Publisher: Oxford University Press, USA
Release Date : 1991
Patterns And Waves written by Peter Grindrod and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Numerical Bifurcation Analysis For Reaction Diffusion Equations
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Author : Zhen Mei
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-06-21
Numerical Bifurcation Analysis For Reaction Diffusion Equations written by Zhen Mei 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 2000-06-21 with Mathematics categories.
This monograph is the first to provide readers with numerical tools for a systematic analysis of bifurcation problems in reaction-diffusion equations. Many examples and figures illustrate analysis of bifurcation scenario and implementation of numerical schemes. Readers will gain a thorough understanding of numerical bifurcation analysis and the necessary tools for investigating nonlinear phenomena in reaction-diffusion equations.
Reaction Diffusion Systems
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Author : Gabriela Caristi
language : en
Publisher: CRC Press
Release Date : 2020-10-07
Reaction Diffusion Systems written by Gabriela Caristi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-07 with Mathematics categories.
"Based on the proceedings of the International Conference on Reaction Diffusion Systems held recently at the University of Trieste, Italy. Presents new research papers and state-of-the-art surveys on the theory of elliptic, parabolic, and hyperbolic problems, and their related applications. Furnishes incisive contribution by over 40 mathematicians representing renowned institutions in North and South America, Europe, and the Middle East."
Spatial Ecology Via Reaction Diffusion Equations
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Author : Robert Stephen Cantrell
language : en
Publisher: John Wiley & Sons
Release Date : 2004-01-09
Spatial Ecology Via Reaction Diffusion Equations written by Robert Stephen Cantrell and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-09 with Mathematics categories.
Many ecological phenomena may be modelled using apparently random processes involving space (and possibly time). Such phenomena are classified as spatial in their nature and include all aspects of pollution. This book addresses the problem of modelling spatial effects in ecology and population dynamics using reaction-diffusion models. * Rapidly expanding area of research for biologists and applied mathematicians * Provides a unified and coherent account of methods developed to study spatial ecology via reaction-diffusion models * Provides the reader with the tools needed to construct and interpret models * Offers specific applications of both the models and the methods * Authors have played a dominant role in the field for years Essential reading for graduate students and researchers working with spatial modelling from mathematics, statistics, ecology, geography and biology.
Global Solutions Of Reaction Diffusion Systems
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Author : Franz Rothe
language : en
Publisher: Springer
Release Date : 2006-12-08
Global Solutions Of Reaction Diffusion Systems written by Franz Rothe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Science categories.
Introduction To Reaction Diffusion Equations
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Author : King-Yeung Lam
language : en
Publisher: Springer Nature
Release Date : 2022-12-01
Introduction To Reaction Diffusion Equations written by King-Yeung Lam and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-01 with Mathematics categories.
This book introduces some basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It is divided into four parts. The first part is an introduction to the maximum principle, the theory of principal eigenvalues for elliptic and periodic-parabolic equations and systems, and the theory of principal Floquet bundles. The second part concerns the applications in spatial ecology. We discuss the dynamics of a single species and two competing species, as well as some recent progress on N competing species in bounded domains. Some related results on stream populations and phytoplankton populations are also included. We also discuss the spreading properties of a single species in an unbounded spatial domain, as modeled by the Fisher-KPP equation. The third part concerns the applications in evolutionary biology. We describe the basic notions of adaptive dynamics, such as evolutionarily stable strategies and evolutionary branching points, in the context of a competition model of stream populations. We also discuss a class of selection-mutation models describing a population structured along a continuous phenotypical trait. The fourth part consists of several appendices, which present a self-contained treatment of some basic abstract theories in functional analysis and dynamical systems. Topics include the Krein-Rutman theorem for linear and nonlinear operators, as well as some elements of monotone dynamical systems and abstract competition systems. Most of the book is self-contained and it is aimed at graduate students and researchers who are interested in the theory and applications of reaction-diffusion equations.
Nonlinear Reaction Diffusion Systems
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Author : Roman Cherniha
language : en
Publisher: Springer
Release Date : 2017-09-18
Nonlinear Reaction Diffusion Systems written by Roman Cherniha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-18 with Mathematics categories.
This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception, parts of the book can also be used in master’s level mathematical biology courses.