Propagation Phenomena in a Bistable Reaction Diffusion System PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Propagation Phenomena in a Bistable Reaction Diffusion System PDF full book. Access full book title Propagation Phenomena in a Bistable Reaction Diffusion System by John Rinzel. Download full books in PDF and EPUB format.
Author: John Rinzel
Publisher:
ISBN:
Category :
Languages : en
Pages : 63
Get Book Here
Book Description
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.
Author: John Rinzel
Publisher:
ISBN:
Category :
Languages : en
Pages : 63
Get Book Here
Book Description
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.
Author: Weiwei Ding
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
This dissertation is concerned with propagation phenomena of some evolution equations in periodic habitats. The main results consist of the following two parts. In the first part, we investigate the spatial spreading phenomena of some spatially periodic integro-difference equations. Firstly, we establish a general theory on the existence of spreading speeds for noncompact evolution systems, under the hypothesis that the linearized systems have principal eigenvalues. Secondly, we introduce the notion of uniform irreducibility for finite Radon measures on the circle. It is shown that, any generalized convolution operator generated by such a measure admits a principal eigenvalue. Finally, applying the above general theories, we prove the existence of spreading speeds for some integro-difference equations with uniformly irreducible dispersal kernels. In the second part, we study the front propagation phenomena of spatially periodic reaction-diffusion equations with bistable nonlinearities. Firstly, we focus on the propagation solutions in the class of pulsating fronts. It is proved that, under various assumptions on the reaction terms, pulsating fronts exist when the spatial period is small or large. We also characterize the sign of the front speeds and we show the global exponential stability of the pulsating fronts with nonzero speed. Secondly, we investigate the propagation solutions in the larger class of transition fronts. It is shown that, under suitable assumptions, transition fronts are reduced to pulsating fronts with nonzero speed. But we also prove the existence of new types of transition fronts which are not pulsating fronts.
Author: Masaharu Taniguchi
Publisher:
ISBN: 9784864970976
Category : Mathematics
Languages : en
Pages : 0
Get Book Here
Book Description
The study on traveling fronts in reaction-diffusion equations is the first step to understand various kinds of propagation phenomena in reaction-diffusion models in natural science. One dimensional traveling fronts have been studied from the 1970s, and multidimensional ones have been studied from around 2005. This volume is a text book for graduate students to start their studies on traveling fronts. Using the phase plane analysis, we study the existence of traveling fronts in several kinds of reaction-diffusion equations. For a nonlinear reaction term, a bistable one is a typical one. For a bistable reaction-diffusion equation, we study the existence and stability of two-dimensional V-form fronts, and we also study pyramidal traveling fronts in three or higher space dimensions. The cross section of a pyramidal traveling front forms a convex polygon. It is known that the limit of a pyramidal traveling front gives a new multidimensional traveling front. For the study the multidimensional traveling front, studying properties of pyramidal traveling fronts plays an important role. In this volume, we study the existence, uniqueness and stability of a pyramidal traveling front as clearly as possible for further studies by graduate students. For a help of their studies, we briefly explain and prove the well-posedness of reaction-diffusion equations and the Schauder estimates and the maximum principles of solutions.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
Author: G. Barles
Publisher:
ISBN:
Category : Differential equations, Parabolic
Languages : en
Pages : 32
Get Book Here
Book Description
Author: Luiz Roberto Evangelista
Publisher: Springer Nature
ISBN: 3031181506
Category : Science
Languages : en
Pages : 411
Get Book Here
Book Description
This book provides a contemporary treatment of the problems related to anomalous diffusion and anomalous relaxation. It collects and promotes unprecedented applications dealing with diffusion problems and surface effects, adsorption-desorption phenomena, memory effects, reaction-diffusion equations, and relaxation in constrained structures of classical and quantum processes. The topics covered by the book are of current interest and comprehensive range, including concepts in diffusion and stochastic physics, random walks, and elements of fractional calculus. They are accompanied by a detailed exposition of the mathematical techniques intended to serve the reader as a tool to handle modern boundary value problems. This self-contained text can be used as a reference source for graduates and researchers working in applied mathematics, physics of complex systems and fluids, condensed matter physics, statistical physics, chemistry, chemical and electrical engineering, biology, and many others.
Author: Antoine Pauthier
Publisher:
ISBN:
Category :
Languages : en
Pages : 131
Get Book Here
Book Description
The aim of this thesis is to study two examples of propagation phenomena in heterogeneous reaction-diffusion equations.The purpose of the first part is to understand the effect of nonlocal exchanges between a line of fast diffusion and a two dimensional environment in which reaction-diffusion of KPP type occurs. The initial model was introduced in 2013 by Berestycki, Roquejoffre, and Rossi. In the first chapter we investigate how the nonlocal coupling between the line and the plane enhances the spreading in the direction of the line; we also investigate how different exchange functions may maximize or not the spreading speed.The second chapter is concerned with the singular limit of nonlocal exchanges that tend to Dirac masses. We show the convergence of the dynamics in a rather strong sense. In the third chapter we study the limit of long range exchanges with constant mass. It gives an infimum for the asymptotic speed of spreading for these models that still could be bigger than the usual KPP spreading speed.The second part of this thesis is concerned with entire solutions for heterogeneous bistable equations.We consider a two dimensional domain infinite in one direction, bounded in the other, that converges to a cylinder as x goes to minus infinity. We prove the existence of an entire solution in such a domain which is the bistable wave for t tends to minus infinity. It also lead us to investigate a one dimensional model with a non-homogeneous reaction term,for which we prove the same property.
Author: Z. Deng
Publisher: CRC Press
ISBN: 100014853X
Category : Mathematics
Languages : en
Pages : 546
Get Book Here
Book Description
This work presents the proceedings from the International Conference on Differential Equations and Control Theory, held recently in Wuhan, China. It provides an overview of current developments in a range of topics including dynamical systems, optimal control theory, stochastic control, chaos, fractals, wavelets and ordinary, partial, functional and stochastic differential equations.
Author: Andreas Liehr
Publisher: Springer Science & Business Media
ISBN: 3642312519
Category : Science
Languages : en
Pages : 227
Get Book Here
Book Description
Why writing a book about a specialized task of the large topic of complex systems? And who will read it? The answer is simple: The fascination for a didactically valuable point of view, the elegance of a closed concept and the lack of a comprehensive disquisition. The fascinating part is that field equations can have localized solutions exhibiting the typical characteristics of particles. Regarding the field equations this book focuses on, the field phenomenon of localized solutions can be described in the context of a particle formalism, which leads to a set of ordinary differential equations covering the time evolution of the position and the velocity of each particle. Moreover, starting from these particle dynamics and making the transition to many body systems, one considers typical phenomena of many body systems as shock waves and phase transitions, which themselves can be described as field phenomena. Such transitions between different level of modelling are well known from conservative systems, where localized solutions of quantum field theory lead to the mechanisms of elementary particle interaction and from this to field equations describing the properties of matter. However, in dissipative systems such transitions have not been considered yet, which is adjusted by the presented book. The elegance of a closed concept starts with the observation of self-organized current filaments in a semiconductor gas discharge system. These filaments move on random paths and exhibit certain particle features like scattering or the formation of bound states. Neither the reasons for the propagation of the filaments nor the laws of the interaction between the filaments can be registered by direct observations. Therefore a model is established, which is phenomenological in the first instance due to the complexity of the experimental system. This model allows to understand the existence of localized structures, their mechanisms of movement, and their interaction, at least, on a qualitative level. But this model is also the starting point for developing a data analysis method that enables the detection of movement and interaction mechanisms of the investigated localized solutions. The topic is rounded of by applying the data analysis to real experimental data and comparing the experimental observations to the predictions of the model. A comprehensive publication covering the interesting topic of localized solutions in reaction diffusion systems in its width and its relation to the well known phenomena of spirals and patterns does not yet exist, and this is the third reason for writing this book. Although the book focuses on a specific experimental system the model equations are as simple as possible so that the discussed methods should be adaptable to a large class of systems showing particle-like structures. Therefore, this book should attract not only the experienced scientist, who is interested in self-organization phenomena, but also the student, who would like to understand the investigation of a complex system on the basis of a continuous description.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 328
Get Book Here
Book Description
Author: Joop Pauwelussen
Publisher:
ISBN:
Category :
Languages : en
Pages : 234
Get Book Here
Book Description
