Traveling Front Solutions In Reaction Diffusion Equations Vol 39
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Traveling Front Solutions in Reaction-Diffusion Equations
| Author | : Masaharu Taniguchi |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2021-05-28 |
| Genre | : Mathematics |
| ISBN | : 9784864970976 |
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
Fractional Dispersive Models and Applications
| Author | : Panayotis G. Kevrekidis |
| Publisher | : Springer Nature |
| Total Pages | : 337 |
| Release | : |
| Genre | : |
| ISBN | : 3031549783 |
Traveling Wave Solutions of Parabolic Systems
| Author | : A. I. Volpert |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 474 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 9780821897577 |
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.
Reaction-diffusion Equations And Their Applications And Computational Aspects - Proceedings Of The China-japan Symposium
| Author | : Tatsien Li |
| Publisher | : World Scientific |
| Total Pages | : 242 |
| Release | : 1997-02-03 |
| Genre | : |
| ISBN | : 9814547840 |
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.
Shock Waves and Reaction—Diffusion Equations
| Author | : Joel Smoller |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 650 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461208734 |
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.
Travelling Waves in Nonlinear Diffusion-Convection Reaction
| Author | : Brian H. Gilding |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 224 |
| Release | : 2004-07-23 |
| Genre | : Mathematics |
| ISBN | : 9783764370718 |
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.
Matched Asymptotic Expansions in Reaction-Diffusion Theory
| Author | : J.A. Leach |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 289 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 0857293966 |
This volume contains a wealth of results and methodologies applicable to a wide range of problems arising in reaction-diffusion theory. It can be viewed both as a handbook, and as a detailed description of the methodology. The authors present new methods based on matched asymptotic expansions.
Reaction-diffusion Waves
| Author | : Arnaud Ducrot |
| Publisher | : Editions Publibook |
| Total Pages | : 119 |
| Release | : 2009 |
| Genre | : Differential operators |
| ISBN | : 2748346319 |
