Traveling Wave Solutions Of Parabolic Systems

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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.

Traveling Wave Solutions Of Parabolic Systems

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Author : Aĭzik Isaakovich Volʹpert
language : ru
Publisher: American Mathematical Society(RI)
Release Date : 1994

Traveling Wave Solutions Of Parabolic Systems written by Aĭzik Isaakovich Volʹpert and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Chemical kinetics categories.

The theory of traveling 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. The main part of the book contains original approaches developed by the authors. Among these are a description of the long-term behavior of the solutions by systems of waves; construction of rotations of vector fields for noncompact operators describing wave solutions; a proof of the existence of waves by the Leray-Schauder method; local, global, and nonlinear stability analyses for some classes of systems; and a determination of the wave velocity by the minimax method and the method of successive approximations. The authors show that wide classes of reaction-diffusion systems can be reduced to so-called monotone and locally monotone systems. This fundamental result allows them to apply the theory to combustion and chemical kinetics. With introductory material accessible to nonmathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.

Travelling Waves In Nonlinear Diffusion Convection Reaction

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Author : Brian H. Gilding
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Travelling Waves In Nonlinear Diffusion Convection Reaction written by Brian H. Gilding and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Nonlinear Systems Of Partial Differential Equations Applications To Life And Physical Sciences

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Author : Anthony W Leung
language : en
Publisher: World Scientific
Release Date : 2009-08-28

Nonlinear Systems Of Partial Differential Equations Applications To Life And Physical Sciences written by Anthony W Leung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-28 with Mathematics categories.

The book presents the theory of diffusion-reaction equations starting from the Volterra-Lotka systems developed in the eighties for Dirichlet boundary conditions. It uses the analysis of applicable systems of partial differential equations as a starting point for studying upper-lower solutions, bifurcation, degree theory and other nonlinear methods. It also illustrates the use of semigroup, stability theorems and W2ptheory. Introductory explanations are included in the appendices for non-expert readers.The first chapter covers a wide range of steady-state and stability results involving prey-predator, competing and cooperating species under strong or weak interactions. Many diagrams are included to easily understand the description of the range of parameters for coexistence. The book provides a comprehensive presentation of topics developed by numerous researchers. Large complex systems are introduced for modern research in ecology, medicine and engineering.Chapter 3 combines the theories of earlier chapters with the optimal control of systems involving resource management and fission reactors. This is the first book to present such topics at research level. Chapter 4 considers persistence, cross-diffusion, and boundary induced blow-up, etc. The book also covers traveling or systems of waves, coupled Navier-Stokes and Maxwell systems, and fluid equations of plasma display. These should be of interest to life and physical scientists.

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 OC International Conference on Reaction-Diffusion Systems and Viscosity SolutionsOCO, held at Providence University, Taiwan, during January 3OCo6, 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 (Japan), N Ishimura (Japan), Shigeaki Koike (Japan), Chu-Pin Lo (Taiwan), Peter Polacik (USA), Kunimochi Sakamoto (Japan), Richard Tsai (USA), Mingxin Wang (China), Yoshio Yamada (Japan), Eiji Yanagida (Japan), and Xiao-Qiang Zhao (Canada).

Propagating Terraces And The Dynamics Of Front Like Solutions Of Reaction Diffusion Equations On R

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Author : Peter Poláčik
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-13

Propagating Terraces And The Dynamics Of Front Like Solutions Of Reaction Diffusion Equations On R written by Peter Poláčik 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 2020-05-13 with Education categories.

The author considers semilinear parabolic equations of the form ut=uxx+f(u),x∈R,t>0, where f a C1 function. Assuming that 0 and γ>0 are constant steady states, the author investigates the large-time behavior of the front-like solutions, that is, solutions u whose initial values u(x,0) are near γ for x≈−∞ and near 0 for x≈∞. If the steady states 0 and γ are both stable, the main theorem shows that at large times, the graph of u(⋅,t) is arbitrarily close to a propagating terrace (a system of stacked traveling fonts). The author proves this result without requiring monotonicity of u(⋅,0) or the nondegeneracy of zeros of f. The case when one or both of the steady states 0, γ is unstable is considered as well. As a corollary to the author's theorems, he shows that all front-like solutions are quasiconvergent: their ω-limit sets with respect to the locally uniform convergence consist of steady states. In the author's proofs he employs phase plane analysis, intersection comparison (or, zero number) arguments, and a geometric method involving the spatial trajectories {(u(x,t),ux(x,t)):x∈R}, t>0, of the solutions in question.

Nonlinear Pde S In Condensed Matter And Reactive Flows

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Author : Henri Berestycki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Nonlinear Pde S In Condensed Matter And Reactive Flows written by Henri Berestycki 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.

Nonlinear partial differential equations abound in modern physics. The problems arising in these fields lead to fascinating questions and, at the same time, progress in understanding the mathematical structures is of great importance to the models. Nevertheless, activity in one of the approaches is not always sufficiently in touch with developments in the other field. The book presents the joint efforts of mathematicians and physicists involved in modelling reactive flows, in particular superconductivity and superfluidity. Certain contributions are fundamental to an understanding of such cutting-edge research topics as rotating Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak turbulence equations, and the propagation of fronts in heterogeneous media.

Theory And Applications Of Partial Functional Differential Equations

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Author : Jianhong Wu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Theory And Applications Of Partial Functional Differential Equations written by Jianhong Wu 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.

Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.

Partial Differential Equations In Ecology

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Author : Sergei Petrovski
language : en
Publisher: MDPI
Release Date : 2021-03-17

Partial Differential Equations In Ecology written by Sergei Petrovski and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-17 with Mathematics categories.

Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.

Newton Methods For Nonlinear Problems

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Author : Peter Deuflhard
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-01-13

Newton Methods For Nonlinear Problems written by Peter Deuflhard 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 2005-01-13 with Mathematics categories.

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.