Download or read book On Steady state Problems for Some Nonlinear Reaction diffusion Systems written by Kimie Nakashima and published by . This book was released on 1999 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Closer Look of Nonlinear Reaction Diffusion Equations written by L. Rajendran and published by Nova Science Publishers. This book was released on 2020-08-26 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: By using mathematical models to describe the physical, biological or chemical phenomena, one of the most common results is either a differential equation or a system of differential equations, together with the correct boundary and initial conditions. The determination and interpretation of their solution are at the base of applied mathematics. Hence the analytical and numerical study of the differential equation is very much essential for all theoretical and experimental researchers, and this book helps to develop skills in this area.Recently non-linear differential equations were widely used to model many of the interesting and relevant phenomena found in many fields of science and technology on a mathematical basis. This problem is to inspire them in various fields such as economics, medical biology, plasma physics, particle physics, differential geometry, engineering, signal processing, electrochemistry and materials science.This book contains seven chapters and practical applications to the problems of the real world. The first chapter is specifically for those with limited mathematical background. Chapter one presents the introduction of non-linear reaction-diffusion systems, various boundary conditions and examples. Real-life application of non-linear reaction-diffusion in different fields with some important non-linear equations is also discussed. In Chapter 2, mathematical preliminaries and various advanced methods of solving non-linear differential equations such as Homotopy perturbation method, variational iteration method, exponential function method etc. are described with examples.Steady and non-steady state reaction-diffusion equations in the plane sheet (chapter 3), cylinder (chapter 4) and spherical (chapter 5) are analyzed. The analytical results published by various researchers in referred journals during 2007-2020 have been addressed in these chapters 4 to 6, and this leads to conclusions and recommendations on what approaches to use on non-linear reaction-diffusion equations.Convection-diffusion problems arise very often in applied sciences and engineering. Non-linear convection-diffusion equations and corresponding analytical solutions in various fields of chemical sciences are discussed in chapter6. Numerical methods are used to provide approximate results for the non-linear problems, and their importance is felt when it is impossible or difficult to solve a given problem analytically. Chapter 7 identifies some of the numerical methods for finding solutions to non-linear differential equations.
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 173 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 Recent Progress on Reaction diffusion Systems and Viscosity Solutions written by Yihong Du and published by World Scientific. This book was released on 2009 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of survey and research articles expanding on the theme of the ?International Conference on Reaction-Diffusion Systems and Viscosity Solutions?, held at Providence University, Taiwan, during January 3?6, 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 (Waseda), N Ishimura (Japan), Shigeaki Koike (Japan), Chu-Pin Lo (Taiwan), Peter Polacik (Minnesota), Kunimochi Sakamoto (Hiroshima), Richard Tsai (Texas), Mingxin Wang (China), Yoshio Yamada (Waseda), Eiji Yanagida (Tohoku), and Xiao-Qiang Zhao (Canada).
Download or read book Reaction Diffusion Systems written by Gabriela Caristi and published by CRC Press. This book was released on 2020-10-07 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Based on the proceedings of the International Conference on Reaction Diffusion Systems held recently at the University of Trieste, Italy. Presents new research papers and state-of-the-art surveys on the theory of elliptic, parabolic, and hyperbolic problems, and their related applications. Furnishes incisive contribution by over 40 mathematicians representing renowned institutions in North and South America, Europe, and the Middle East."
Download or read book Nonlinear Systems Of Partial Differential Equations Applications To Life And Physical Sciences written by Anthony W Leung and published by World Scientific. This book was released on 2009-08-28 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Differential Equations of Chemically Reacting Systems written by George R. Gavalas and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years considerable interest has developed in the mathe matical analysis of chemically reacting systems both in the absence and in the presence of diffusion. Earlier work has been limited to simple problems amenable to closed form solutions, but now the computer permits the numerical solution of complex systems of nonlinear differ ential equations. The numerical approach provides quantitative infor mation, but for practical reasons it must be limited to a rather narrow range of the parameters of the problem. Consequently, it is desirable to obtain broader qualitative information about the solutions by in vestigating from a more fundamental mathematical point of view the structure of the differential equations. This theoretical approach can actually complement and guide the computational approach by narrow ing down trial and error procedures, pinpointing singularities and suggesting methods for handling them. The study of the structure of the differential equations may also clarify some physical principles and suggest new experiments. A serious limitation ofthe theoretical approach is that many of the results obtained, such as the sufficient conditions for the stability of the steady state, turn out to be very conservative. Thus the theoretical and computational approaches are best used to gether for the purpose of understanding, designing, and controlling chemically reacting systems. The present monograph is intended as a contribution to the theory of the differential equations describing chemically reacting systems.
Download or read book Nonlinear Parabolic and Elliptic Equations written by C.V. Pao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.
Download or read book Problems in Nonlinear Diffusion written by Antonio Fasano and published by Springer. This book was released on 2006-11-14 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Superlinear Parabolic Problems written by Pavol Quittner and published by Springer Science & Business Media. This book was released on 2007-12-16 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The book is self-contained and up-to-date, taking special care on the didactical preparation of the material. It is devoted to problems that are intensively studied but have not been treated thus far in depth in the book literature.
Download or read book The Existence of Multiple Steady state Solutions of a Reaction diffusion Equation written by Isobel M. Lee and published by . This book was released on 1988 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Diffusion written by Homer Franklin Walker and published by Pitman Publishing. This book was released on 1977 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematics of Diffusion written by Wei-Ming Ni and published by SIAM. This book was released on 2011-10-13 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. The Mathematics of Diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity. The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusion-driven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements and spatial heterogeneity in the classical Lotka–Volterra competition systems. Interspersed throughout the book are many simple, fundamental and important open problems for readers to investigate.
Download or read book Variational Convergence and Stochastic Homogenization of Nonlinear Reaction Diffusion Problems written by OMAR ANZA. MANDALLENA HAFSA (JEAN PHILIPPE. MICHAILLE, GERARD.) and published by . This book was released on 2022-06-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A substantial number of problems in physics, chemical physics, and biology, are modeled through reaction-diffusion equations to describe temperature distribution or chemical substance concentration. For problems arising from ecology, sociology, or population dynamics, they describe the density of some populations or species. In this book the state variable is a concentration, or a density according to the cases. The reaction function may be complex and include time delays terms that model various situations involving maturation periods, resource regeneration times, or incubation periods. The dynamics may occur in heterogeneous media and may depend upon a small or large parameter, as well as the reaction term. From a purely formal perspective, these parameters are indexed by n. Therefore, reaction-diffusion equations give rise to sequences of Cauchy problems.The first part of the book is devoted to the convergence of these sequences in a sense made precise in the book. The second part is dedicated to the specific case when the reaction-diffusion problems depend on a small parameter ∊ₙ intended to tend towards 0. This parameter accounts for the size of small spatial and randomly distributed heterogeneities. The convergence results obtained in the first part, with additionally some probabilistic tools, are applied to this specific situation. The limit problems are illustrated through biological invasion, food-limited or prey-predator models where the interplay between environment heterogeneities in the individual evolution of propagation species plays an essential role. They provide a description in terms of deterministic and homogeneous reaction-diffusion equations, for which numerical schemes are possible.
Download or read book The Existence of Multiple Steady state Solutions of a Reaction diffusion Equation written by Isobel M. Lee and published by . This book was released on 1988 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Djairo G de Figueiredo Selected Papers written by Djairo G. de Figueiredo and published by Springer Science & Business Media. This book was released on 2014-01-07 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of selected papers by the prominent Brazilian mathematician Djairo G. de Figueiredo, who has made significant contributions in the area of Differential Equations and Analysis. His work has been highly influential as a challenge and inspiration to young mathematicians as well as in development of the general area of analysis in his home country of Brazil. In addition to a large body of research covering a variety of areas including geometry of Banach spaces, monotone operators, nonlinear elliptic problems and variational methods applied to differential equations, de Figueiredo is known for his many monographs and books. Among others, this book offers a sample of the work of Djairo, as he is commonly addressed, advancing the study of superlinear elliptic problems (both scalar and system cases), including questions on critical Sobolev exponents and maximum principles for non-cooperative elliptic systems in Hamiltonian form.
Download or read book Applied Theory of Functional Differential Equations written by V. Kolmanovskii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to the properties of functional differential equations and their applications in diverse fields such as immunology, nuclear power generation, heat transfer, signal processing, medicine and economics. In particular, it deals with problems and methods relating to systems having a memory (hereditary systems). The book contains eight chapters. Chapter 1 explains where functional differential equations come from and what sort of problems arise in applications. Chapter 2 gives a broad introduction to the basic principle involved and deals with systems having discrete and distributed delay. Chapters 3-5 are devoted to stability problems for retarded, neutral and stochastic functional differential equations. Problems of optimal control and estimation are considered in Chapters 6-8. For applied mathematicians, engineers, and physicists whose work involves mathematical modeling of hereditary systems. This volume can also be recommended as a supplementary text for graduate students who wish to become better acquainted with the properties and applications of functional differential equations.
