Download or read book Propagating Waves in Reaction Cross diffusion Systems written by Abdullah Mohammed Aldurayhim and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Propagation of Waves in Reaction diffusion Systems Applications to Biology and Chemistry written by J. H. Merkin and published by . This book was released on 2007 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Propagating Waves and Target Patterns in Chemical Systems written by Paul C. Fife and published by . This book was released on 1980 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of models for target patterns (concentric circular waves emanating from a point called the leading center) is constructed in the context of singularly perturbed reaction-diffusion systems of partial differential equations. First, the theory of wave fronts is detailed for scalar equations and systems of equations. A scaling method reduces complex waves to the consideration of a group of simple wave phenomena. It is shown that expanding wave fronts can be generated spontaneously at a point. This process, together with the laws of their subsequent motion, reduces the problem to an ordinary differential initial value problem, whose solution is required to have certain properties. A discussion is given of the connection between these results and experimental observations. (Author).
Download or read book Reaction diffusion Waves written by Arnaud Ducrot and published by Editions Publibook. This book was released on 2009 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generation and Propagation of Interfaces in Reaction Diffusion Systems written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1990 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wave Propagation in a Coupled Reaction diffusion System microform written by Pak Ki Jacky Li and published by National Library of Canada = Bibliothèque nationale du Canada. This book was released on 2002 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Travelling Waves in Nonlinear Diffusion Convection Reaction written by Brian H. Gilding and published by Birkhäuser. This book was released on 2012-12-06 with total page 214 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 Propagation Phenomena in a Bistable Reaction Diffusion System written by John Rinzel and published by . This book was released on 1981 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Propagation Failure in Discrete Reaction diffusion Systems written by Victoria Booth and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Shock Waves and Reaction Diffusion Equations written by Joel Smoller and published by . This book was released on 1994-10-14 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wavefront Propagation for Reaction diffusion Systems of PDE written by G. Barles and published by . This book was released on 1989 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Patterns and Waves written by Peter Grindrod and published by . This book was released on 1996 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Instabilities and Propagation Properties in Two component Reaction diffusion Systems written by Samir Shams Eldeen and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis deals with a detailed linear analysis for a two-component reaction-diffusion system with constant diffusion coefficients. A comprehensive linear stability analysis results in three types of instabilities: (1) stationary periodic instability, (2) oscillatory uniform and (3) stationary uniform. The first instability involves pattern formation and the other two do not. Precise parameter regimes are identified for each. Travelling wave analysis is performed for the system and a detailed and comprehensive analysis is undertaken of a linear mechanism governing the development and propagation of nonlinear patterns. This analysis focuses on a linear selection mechanism that gives some insights into the selected speed of invasion of an unstable state by a stable one, as described both by a fixed form of travelling wave and by a modulated travelling wave.
Download or read book Cross Diffusion Systems written by Dung Le and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-10-24 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new findings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenberg inequality involving BMO norms is improved and new techniques are covered that will be of interest. This book also provides many open problems suitable for interested Ph.D students.
Download or read book Dichotomies in Stability Theory written by W. A. Coppel and published by Springer. This book was released on 2006-11-15 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Large Deviation Principle and Wave Front Propagation for a Reaction diffusion Equation written by Sara Ianda Correa Carmona and published by . This book was released on 1992 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fast Propagation in Reaction diffusion Equations with Fractional Diffusion written by Anne-Charline Coulon Chalmin and published by . This book was released on 2014 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focuses on the long time behaviour, and more precisely on fast propagation, in Fisher-KPP reaction diffusion equations involving fractional diffusion. This type of equation arises, for example, in spreading of biological species. Under some specific assumptions, the population invades the medium and we want to understand at which speed this invasion takes place when fractional diffusion is at stake. To answer this question, we set up a new method and apply it on different models. In a first part, we study two different problems, both including fractional diffusion : Fisher-KPP models in periodic media and cooperative systems. In both cases, we prove, under additional assumptions, that the solution spreads exponentially fast in time and we find the precise exponent of propagation. We also carry out numerical simulations to investigate the dependence of the speed of propagation on the initial condition. In a second part, we deal with a two dimensional environment, where reproduction of Fisher-KPP type and usual diffusion occur, except on a line of the plane, on which fractional diffusion takes place. The plane is referred to as "the field" and the line to "the road", as a reference to the biological situations we have in mind. We prove that the speed of propagation is exponential in time on the road, whereas it depends linearly on time in the field. The expansion shape of the level sets in the field is investigated through numerical simulations.
