Threshold Phenomena For A Reaction Diffusion System
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Threshold Phenomena For A Reaction Diffusion System
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Author : David Terman
language : en
Publisher:
Release Date : 1981
Threshold Phenomena For A Reaction Diffusion System written by David Terman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Propagation Phenomena In A Bistable Reaction Diffusion System
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Author : John Rinzel
language : en
Publisher:
Release Date : 1981
Propagation Phenomena In A Bistable Reaction Diffusion System written by John Rinzel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Consideration is given to a system of reaction diffusion equations which have qualitative significance for several applications including nerve conduction and distributed chemical/biochemical systems. These equations are of the FitzHugh-Nagumo type and contain three parameters. For certain ranges of the parameters the system exhibits two stable singular points. A singular perturbation construction is given to illustrate that there may exist both pulse type and transition type traveling waves. A complete, rigorous, description of which of these waves exist for a given set of parameters and how the velocities of the waves vary with the parameters is given for the case when the system has a piecewise linear nonlinearity. Numerical results of solutions to these equations are also presented. These calculations illustrate how waves are generated from initial data, how they interact during collisions, and how they are influenced by local disturbances and boundary conditions.
Local Existence For The Cauchy Problem Of A Reaction Diffusion System With Discontinuous Nonlinearity
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Author : David Terman
language : en
Publisher:
Release Date : 1981
Local Existence For The Cauchy Problem Of A Reaction Diffusion System With Discontinuous Nonlinearity written by David Terman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
The most famous model for nerve conduction is due to Hodgkin and Huxley. However, a mathematical analysis of their model has proven very difficult. The complexity of the Hodgkin and Huxley model has led a number of other authors to introduce simpler models. In this report we consider one such simplification. It has been demonstrated (experimentally) that impulses in the nerve axon travel with constant shape and velocity. Mathematically, this corresponds to traveling wave solutions. A number of authors have proven that the mathematical equations considered here do possess traveling wave solutions. Another property of impulses in the nerve axon is the existence of a threshold phenomenon. This corresponds to the biological fact that a minimum stimulus is needed to trigger an impulse. Here we prove some preliminary results which will be used in a later report when it is demonstrated that the equations under study do indeed exhibit a threshold phenomenon.
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.
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 Science categories.
. . . the progress of physics will to a large extent depend on the progress of nonlinear mathe matics, of methods to solve nonlinear equations . . . and therefore we can learn by comparing different nonlinear problems. WERNER HEISENBERG I undertook to write this book for two reasons. First, I wanted to make easily available the basics of both the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by C. Conley. These important subjects seem difficult to learn since the results are scattered throughout the research journals. 1 Second, I feel that there is a need to present the modern methods and ideas in these fields to a wider audience than just mathe maticians. Thus, the book has some rather sophisticated aspects to it, as well as certain textbook aspects. The latter serve to explain, somewhat, the reason that a book with the title Shock Waves and Reaction-Diffusion Equations has the first nine chapters devoted to linear partial differential equations. More precisely, I have found from my classroom experience that it is far easier to grasp the subtleties of nonlinear partial differential equations after one has an understanding of the basic notions in the linear theory. This book is divided into four main parts: linear theory, reaction diffusion equations, shock wave theory, and the Conley index, in that order. Thus, the text begins with a discussion of ill-posed problems.
Nonlinear Parabolic And Elliptic Equations
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Author : C.V. Pao
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Parabolic And Elliptic Equations written by C.V. Pao 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.
In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.
Traveling Wave Solutions Of Parabolic Systems
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Author : A. I. Volpert
language : en
Publisher: American Mathematical Soc.
Release Date :
Traveling Wave Solutions Of Parabolic Systems written by A. I. Volpert and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
The theory of travelling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. With introductory material accessible to non-mathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.
Collective Phenomena Of Coupled Lattice Maps
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Author : James David Keeler
language : en
Publisher:
Release Date : 1987
Collective Phenomena Of Coupled Lattice Maps written by James David Keeler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Computer simulation categories.
Recent Progress On Reaction Diffusion Systems And Viscosity Solutions
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Author : Yihong Du
language : en
Publisher: World Scientific
Release Date : 2009
Recent Progress On Reaction Diffusion Systems And Viscosity Solutions written by Yihong Du and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This book consists of survey and research articles expanding on the theme of the ?International Conference on Reaction-Diffusion Systems and Viscosity Solutions?, held at Providence University, Taiwan, during January 3?6, 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 (Waseda), N Ishimura (Japan), Shigeaki Koike (Japan), Chu-Pin Lo (Taiwan), Peter Polacik (Minnesota), Kunimochi Sakamoto (Hiroshima), Richard Tsai (Texas), Mingxin Wang (China), Yoshio Yamada (Waseda), Eiji Yanagida (Tohoku), and Xiao-Qiang Zhao (Canada).
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.