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 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 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 Nonlinear Reaction Diffusion Systems written by Roman Cherniha and published by Springer. This book was released on 2017-09-18 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Waves in reaction diffusion written by Joop Pauwelussen and published by . This book was released on 1981 with total page 234 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 Nonlinear Waves in Reaction Diffusion Systems written by and published by . This book was released on 1999 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wavefronts in reaction diffusion systems. We obtain new results such as the possibility of spatial oscillations in the wavefront shape for certain values of the system parameters and high enough wavefront speeds. We also generalize earlier known results concerning the minimum wavefront speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piece-wise linear representation of the nonlinearity.
Download or read book R umliche Aspekte intrazellul rer Signal bertragung und Musterbildung in der Glykolyse written by Ronny Straube and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Die vorliegende Arbeit behandelt verschiedene Aspekte der raum-zeitlichen Musterbildung in biologischen oder biologisch motivierten Reaktions-Diffusions-Systemen. Die hierbei auftretenden Muster werden entweder durch die, dem System auferlegten, Randbedingungen oder durch diffusive Kopplung nichtlinearer biochemischer Reaktionen hervorgerufen. Im ersten Teil der Arbeit werden Systeme in singular gestorten zwei- oder drei-dimensionalen Gebieten untersucht. Das sind Gebiete mit kleinen Lochern im Innern oder auf dem Rand des Definitionsgebietes. Mit Hilfe asymptotischer Methoden wird gezeigt, dass sich die Locher wie Punktsingularitaten verhalten, die durch entsprechende Greensche oder Neumann Funktionen beschrieben werden konnen. Es werden asymptotische Losungen fur durch Signalmolekule hervorgerufene intrazellulare Konzentrationsgradienten sowie fur die mittlere Verweilzeit diffundierender Molekule in der Gegenwart mehrerer, kleiner absorbierender Kompartimente (Locher) fur verschiedene Gebiete konstruiert. Im zweiten Teil der Arbeit wird am Beispiel der Entstehung einwarts rotierender Spiralwellen (Antispiralen) in der Glykolyse untersucht, wie sich bestimmte molekulare Reaktionsmechanismen auf die im System entstehenden raum-zeitlichen Muster auswirken. Zu diesem Zweck werden die Parameter einer zugeordneten komplexen Ginzburg-Landau Gleichung fur verschiedene Mechanismen der Produktaktivierung der Phosphofruktokinase (PFK) explizit berechnet und die entsprechenden Phasendiagramme miteinander verglichen. Die Analyse zeigt, dass das Auftreten von Antispiralen sowohl vom PFK-Aktivierungsmechanismus als auch von der Anzahl der PFK-Untereinheiten abhangt.
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 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 Handbook of Differential Equations Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2009-04-29 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Differential Equations: Evolutionary Equations is the last text of a five-volume reference in mathematics and methodology. This volume follows the format set by the preceding volumes, presenting numerous contributions that reflect the nature of the area of evolutionary partial differential equations. The book is comprised of five chapters that feature the following: A thorough discussion of the shallow-equations theory, which is used as a model for water waves in rivers, lakes and oceans. It covers the issues of modeling, analysis and applications • Evaluation of the singular limits of reaction-diffusion systems, where the reaction is fast compared to the other processes; and applications that range from the theory of the evolution of certain biological processes to the phenomena of Turing and cross-diffusion instability Detailed discussion of numerous problems arising from nonlinear optics, at the high-frequency and high-intensity regime • Geometric and diffractive optics, including wave interactions Presentation of the issues of existence, blow-up and asymptotic stability of solutions, from the equations of solutions to the equations of linear and non-linear thermoelasticity Answers to questions about unique space, such as continuation and backward uniqueness for linear second-order parabolic equations. Research mathematicians, mathematics lecturers and instructors, and academic students will find this book invaluable Review of new results in the area Continuation of previous volumes in the handbook series covering evolutionary PDEs New content coverage of DE applications
Download or read book Traveling Wave Solutions of Parabolic Systems written by A. I. Volpert and published by American Mathematical Soc.. This book was released on with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Elliptic Partial Differential Equations written by Vitaly Volpert and published by Springer. This book was released on 2014-05-10 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt: If we had to formulate in one sentence what this book is about, it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equations and new topics such as nonlocal equations and multi-scale models in biology will be considered.
