Download or read book Introduction to Reaction Diffusion Equations written by King-Yeung Lam and published by Springer Nature. This book was released on 2022-12-01 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Nonlinear PDEs written by Marius Ghergu and published by Springer Science & Business Media. This book was released on 2011-10-21 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics,, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and other fields of science and technology and is a comprehensive introduction to the theory of nonlinear partial differential equations and its main principles also presents their real-life applications in various contexts: mathematical physics, chemistry, mathematical biology, and population genetics. Based on the authors' original work, this volume provides an overview of the field, with examples suitable for researchers but also for graduate students entering research. The method of presentation appeals to readers with diverse backgrounds in partial differential equations and functional analysis. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. The content demonstrates in a firm way that partial differential equations can be used to address a large variety of phenomena occurring in and influencing our daily lives. The extensive reference list and index make this book a valuable resource for researchers working in a variety of fields and who are interested in phenomena modeled by nonlinear partial differential equations.​

Download or read book A Short History of Mathematical Population Dynamics written by Nicolas Bacaër and published by Springer Science & Business Media. This book was released on 2011-02-01 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recently grown thanks to the simulation capacity offered by modern computers. This book traces the history of population dynamics---a theoretical subject closely connected to genetics, ecology, epidemiology and demography---where mathematics has brought significant insights. It presents an overview of the genesis of several important themes: exponential growth, from Euler and Malthus to the Chinese one-child policy; the development of stochastic models, from Mendel's laws and the question of extinction of family names to percolation theory for the spread of epidemics, and chaotic populations, where determinism and randomness intertwine. The reader of this book will see, from a different perspective, the problems that scientists face when governments ask for reliable predictions to help control epidemics (AIDS, SARS, swine flu), manage renewable resources (fishing quotas, spread of genetically modified organisms) or anticipate demographic evolutions such as aging.

Download or read book Reaction diffusion Equations And Their Applications And Computational Aspects Proceedings Of The China japan Symposium written by Tatsien Li and published by World Scientific. This book was released on 1997-02-03 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the symposium was to provide a forum for presenting and discussing recent developments and trends in Reaction-diffusion Equations and to promote scientific exchanges among mathematicians in China and in Japan, especially for the younger generation. The topics discussed were: Layer dynamics, Traveling wave solutions and its stability, Equilibrium solutions and its limit behavior (stability), Bifurcation phenomena, Computational solutions, and Infinite dimensional dynamical system.

Download or read book Spatial Ecology via Reaction Diffusion Equations written by Robert Stephen Cantrell and published by John Wiley & Sons. This book was released on 2004-01-09 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Dynamics of Internal Layers and Diffusive Interfaces written by Paul C. Fife and published by SIAM. This book was released on 1988-01-01 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interfacial phenomena are commonplace in physics, chemistry, biology, and in various disciplines bridging these fields. They occur whenever a continuum is present which can exist in at least two different chemical or physical "states," and there is some mechanism which generates or enforces a spatial separation between these states. The separation boundary is then called an interface. In the examples studied here, the separation boundary, and its internal structure, result from the balance between two opposing tendencies: a diffusive effect which attempts to mix and smooth the properties of the material, and a physical or chemical mechanism which works to drive it to one or the other pure state. This volume is unique in that the treatment of flames, as well as internal layer dynamics "including curvature effects," is more detailed and systematic than in publications.

Download or read book Shock Waves and Reaction Diffusion Equations written by Joel Smoller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Aspects of Reacting and Diffusing Systems written by P. C. Fife and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. These equations often take the form of systems of nonlinear parabolic partial d- ferential equations, or reaction-diffusion equations, when there is diffusion of chemical substances involved. A good overview of this endeavor can be had by re- ing the two volumes by R. Aris (1975), who himself was one of the main contributors to the theory. Enthusiasm for the models developed has been shared by parts of the mathematical community, and these models have, in fact, provided motivation for some beautiful mathematical results. There are analogies between chemical reactors and certain biological systems. One such analogy is rather obvious: a single living organism is a dynamic structure built of molecules and ions, many of which react and diffuse. Other analogies are less obvious; for example, the electric potential of a membrane can diffuse like a chemical, and of course can interact with real chemical species (ions) which are transported through the membrane. These facts gave rise to Hodgkin's and Huxley's celebrated model for the propagation of nerve signals. On the level of populations, individuals interact and move about, and so it is not surprising that here, again, the simplest continuous space-time interaction-migration models have the same g- eral appearance as those for diffusing and reacting chemical systems.

Download or read book Parabolic Equations in Biology written by Benoît Perthame and published by Springer. This book was released on 2015-09-09 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

Download or read book Determination of Complex Reaction Mechanisms written by John Ross and published by Oxford University Press. This book was released on 2006 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a chemical system with many chemical species several questions can be asked: what species react with other species: in what temporal order: and with what results? These questions have been asked for over one hundred years about simple and complex chemical systems, and the answers constitute the macroscopic reaction mechanism. In Determination of Complex Reaction Mechanisms authors John Ross, Igor Schreiber, and Marcel Vlad present several systematic approaches for obtaining information on the causal connectivity of chemical species, on correlations of chemical species, on the reaction pathway, and on the reaction mechanism.Basic pulse theory is demonstrated and tested in an experiment on glycolysis. In a second approach, measurements on time series of concentrations are used to construct correlation functions and a theory is developed which shows that from these functions information may be inferred on the reaction pathway, the reaction mechanism, and the centers of control in that mechanism. A third approach is based on application of genetic algorithm methods to the study of the evolutionary development of a reaction mechanism, to the attainment given goals in a mechanism, and to the determination of a reaction mechanism and rate coefficients by comparison with experiment. Responses of non-linear systems to pulses or other perturbations are analyzed, and mechanisms of oscillatory reactions are presented in detail. The concluding chapters give an introduction to bioinformatics and statistical methods for determining reaction mechanisms.

Download or read book Recent Progress on Reaction diffusion Systems and Viscosity Solutions written by Yihong Du and published by World Scientific. This book was released on 2009 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of survey and research articles expanding on the theme of the OC International Conference on Reaction-Diffusion Systems and Viscosity SolutionsOCO, held at Providence University, Taiwan, during January 3OCo6, 2007. It is a carefully selected collection of articles representing the recent progress of some important areas of nonlinear partial differential equations. The book is aimed for researchers and postgraduate students who want to learn about or follow some of the current research topics in nonlinear partial differential equations. The contributors consist of international experts and some participants of the conference, including Nils Ackermann (Mexico), Chao-Nien Chen (Taiwan), Yihong Du (Australia), Alberto Farina (France), Hitoshi Ishii (Japan), N Ishimura (Japan), Shigeaki Koike (Japan), Chu-Pin Lo (Taiwan), Peter Polacik (USA), Kunimochi Sakamoto (Japan), Richard Tsai (USA), Mingxin Wang (China), Yoshio Yamada (Japan), Eiji Yanagida (Japan), and Xiao-Qiang Zhao (Canada).

Download or read book Travelling Waves in Nonlinear Diffusion Convection Reaction written by Brian H. Gilding and published by Springer Science & Business Media. This book was released on 2004-07-23 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph has grown out of research we started in 1987, although the foun dations were laid in the 1970's when both of us were working on our doctoral theses, trying to generalize the now classic paper of Oleinik, Kalashnikov and Chzhou on nonlinear degenerate diffusion. Brian worked under the guidance of Bert Peletier at the University of Sussex in Brighton, England, and, later at Delft University of Technology in the Netherlands on extending the earlier mathematics to include nonlinear convection; while Robert worked at Lomonosov State Univer sity in Moscow under the supervision of Anatolii Kalashnikov on generalizing the earlier mathematics to include nonlinear absorption. We first met at a conference held in Rome in 1985. In 1987 we met again in Madrid at the invitation of Ildefonso Diaz, where we were both staying at 'La Residencia'. As providence would have it, the University 'Complutense' closed down during this visit in response to student demonstra tions, and, we were very much left to our own devices. It was natural that we should gravitate to a research topic of common interest. This turned out to be the characterization of the phenomenon of finite speed of propagation for nonlin ear reaction-convection-diffusion equations. Brian had just completed some work on this topic for nonlinear diffusion-convection, while Robert had earlier done the same for nonlinear diffusion-absorption. There was no question but that we bundle our efforts on the general situation.

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.

Download or read book Integrodifference Equations in Spatial Ecology written by Frithjof Lutscher and published by Springer Nature. This book was released on 2019-10-30 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first thorough introduction to and comprehensive treatment of the theory and applications of integrodifference equations in spatial ecology. Integrodifference equations are discrete-time continuous-space dynamical systems describing the spatio-temporal dynamics of one or more populations. The book contains step-by-step model construction, explicitly solvable models, abstract theory and numerical recipes for integrodifference equations. The theory in the book is motivated and illustrated by many examples from conservation biology, biological invasions, pattern formation and other areas. In this way, the book conveys the more general message that bringing mathematical approaches and ecological questions together can generate novel insights into applications and fruitful challenges that spur future theoretical developments. The book is suitable for graduate students and experienced researchers in mathematical ecology alike.

Download or read book Reaction diffusion Equations and Their Applications to Biology written by N. F. Britton and published by . This book was released on 1986 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Download or read book Population Genetics written by John H. Gillespie and published by JHU Press. This book was released on 2004-08-06 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description