The Dynamics Of Front Propagation In Nonlocal Reaction Diffusion Equations
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The Dynamics Of Front Propagation In Nonlocal Reaction Diffusion Equations
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Author : Jean-Michel Roquejoffre
language : en
Publisher: Springer Nature
Release Date : 2024-12-18
The Dynamics Of Front Propagation In Nonlocal Reaction Diffusion Equations written by Jean-Michel Roquejoffre and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-18 with Mathematics categories.
The book provides a self-contained and complete description of the long time evolution of the solutions to a class of one-dimensional reaction–diffusion equations, in which the diffusion is given by an integral operator. The underlying motivation is the mathematical analysis of models for biological invasions. The model under study, while simple looking, is of current use in real-life situations. Interestingly, it arises in totally different contexts, such as the study of branching random walks in probability theory. While the model has attracted a lot of attention, and while many partial results about the time-asymptotic behaviour of its solutions have been proved over the last decades, some basic questions on the sharp asymptotics have remained unanswered. One ambition of this monograph is to close these gaps. In some of the situations that we envisage, the level sets organise themselves into an invasion front that is asymptotically linear in time, up to a correction that converges exponentially in time to a constant. In other situations that constitute the main and newest part of the work, the correction is asymptotically logarithmic in time. Despite these apparently different behaviours, there is an underlying common way of thinking that is underlined. At the end of each chapter, a long set of problems is proposed, many of them rather elaborate and suitable for master's projects or even the first question in a PhD thesis. Open questions are also discussed. The ideas presented in the book apply to more elaborate systems modelling biological invasions or the spatial propagation of epidemics. The models themselves may be multidimensional, but they all have in common a mechanism imposing the propagation in a given direction; examples are presented in the problems that conclude each chapter. These ideas should also be useful in the treatment of further models that we are not able to envisage for the time being. The book is suitable for graduate or PhD students as well as researchers.
The Dynamics Of Front Propagation In Nonlocal Reaction Diffusion Equations
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Author : Jean-Michel Roquejoffre
language : en
Publisher:
Release Date : 2025-01-23
The Dynamics Of Front Propagation In Nonlocal Reaction Diffusion Equations written by Jean-Michel Roquejoffre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-23 with Language Arts & Disciplines categories.
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.
Elliptic Partial Differential Equations
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Author : Vitaly Volpert
language : en
Publisher: Springer
Release Date : 2014-05-10
Elliptic Partial Differential Equations written by Vitaly Volpert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
Iciam 91
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Author : Robert E. O'Malley
language : en
Publisher: SIAM
Release Date : 1992-01-01
Iciam 91 written by Robert E. O'Malley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
Proceedings -- Computer Arithmetic, Algebra, OOP.
Processionary Moths And Climate Change An Update
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Author : Alain Roques
language : en
Publisher: Springer
Release Date : 2014-10-10
Processionary Moths And Climate Change An Update written by Alain Roques and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-10 with Science categories.
Because of its peculiar biology, its negative impacts on forestry, and its urticating larvae affecting human and animal health, pine processionary moth has largely been studied in many European countries during the last century. However, knowledge remained scattered and no synthesis has ever been published. Since the IPCC retained the moth as one of the two insect indicators of climate change because of its expansion with warming up, filling this gap became increasingly important. Led by INRA, this book associates 101 authors from 22 countries of Europe, Minor Asia and North Africa, combining all the concerned research fields (entomology, ecology, genetics, mathematical modelling, medical and veterinary science, pest management) in a multidisciplinary approach to understand and model the processes underlying past, present and future moth expansion and to propose adapted management methods. Besides, the major biological patterns of the related processionary species are also detailed.
Nonlocal Diffusion Problems
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Author : Fuensanta Andreu-Vaillo
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Nonlocal Diffusion Problems written by Fuensanta Andreu-Vaillo 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 2010 with Mathematics categories.
Nonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems are also of great interest for their purely mathematical content. This book presents recent results on nonlocal evolution equations with different boundary conditions, starting with the linear theory and moving to nonlinear cases, including two nonlocal models for the evolution of sandpiles. Both existence and uniqueness of solutions are considered, as well as their asymptotic behaviour. Moreover, the authors present results concerning limits of solutions of the nonlocal equations as a rescaling parameter tends to zero. With these limit procedures the most frequently used diffusion models are recovered: the heat equation, the $p$-Laplacian evolution equation, the porous media equation, the total variation flow, a convection-diffusion equation and the local models for the evolution of sandpiles due to Aronsson-Evans-Wu and Prigozhin. Readers are assumed to be familiar with the basic concepts and techniques of functional analysis and partial differential equations. The text is otherwise self-contained, with the exposition emphasizing an intuitive understanding and results given with full proofs. It is suitable for graduate students or researchers. The authors cover a subject that has received a great deal of attention in recent years. The book is intended as a reference tool for a general audience in analysis and PDEs, including mathematicians, engineers, physicists, biologists, and others interested in nonlocal diffusion problems.
Reaction Diffusion Waves
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Author : Arnaud Ducrot
language : en
Publisher: Editions Publibook
Release Date : 2009
Reaction Diffusion Waves written by Arnaud Ducrot and has been published by Editions Publibook this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Differential operators categories.
Fractional Derivatives With Mittag Leffler Kernel
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Author : José Francisco Gómez
language : en
Publisher: Springer
Release Date : 2019-02-13
Fractional Derivatives With Mittag Leffler Kernel written by José Francisco Gómez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-13 with Technology & Engineering categories.
This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel. The different contributions, written by applied mathematicians, physicists and engineers, offers a snapshot of recent research in the field, highlighting the current methodological frameworks together with applications in different fields of science and engineering, such as chemistry, mechanics, epidemiology and more. It is intended as a timely guide and source of inspiration for graduate students and researchers in the above-mentioned areas.
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).