On Cauchy Problems Of Reaction Diffusion Equations
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On Cauchy Problems Of Reaction Diffusion Equations
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Author : Xuefeng Wang
language : en
Publisher:
Release Date : 1990
On Cauchy Problems Of Reaction Diffusion Equations written by Xuefeng Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Reaction Diffusion Systems
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Author : Gabriela Caristi
language : en
Publisher: CRC Press
Release Date : 2020-10-07
Reaction Diffusion Systems written by Gabriela Caristi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-07 with Mathematics categories.
"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."
Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction Diffusion Problems
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Author : Omar Anza Hafsa
language : en
Publisher: World Scientific
Release Date : 2022-06-21
Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction Diffusion Problems written by Omar Anza Hafsa and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-21 with Mathematics categories.
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.
The Cauchy Problem For Non Lipschitz Semi Linear Parabolic Partial Differential Equations
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Author : J. C. Meyer
language : en
Publisher: Cambridge University Press
Release Date : 2015-10-22
The Cauchy Problem For Non Lipschitz Semi Linear Parabolic Partial Differential Equations written by J. C. Meyer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-22 with Mathematics categories.
A monograph containing significant new developments in the theory of reaction-diffusion systems, particularly those arising in chemistry and life sciences.
Reaction Diffusion Equations And Their Applications To Biology
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Author : N. F. Britton
language : en
Publisher:
Release Date : 1986
Reaction Diffusion Equations And Their Applications To Biology written by N. F. Britton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Science categories.
Although the book is largely self-contained, some knowledge of the mathematics of differential equations is necessary. Thus the book is intended for mathematicians who are interested in the application of their subject to the biological sciences and for biologists with some mathematical training. It is also suitable for postgraduate mathematics students and for undergraduate mathematicians taking a course in mathematical biology. Increasing use of mathematics in developmental biology, ecology, physiology, and many other areas in the biological sciences has produced a need for a complete, mathematical reference for laboratory practice. In this volume, biological scientists will find a rich resource of interesting applications and illustrations of various mathematical techniques that can be used to analyze reaction-diffusion systems. Concepts covered here include:**systems of ordinary differential equations**conservative systems**the scalar reaction-diffusion equation**analytic techniques for systems of parabolic partial differential equations**bifurcation theory**asymptotic methods for oscillatory systems**singular perturbations**macromolecular carriers -- asymptotic techniques.
The Cauchy Problem For Non Lipschitz Semi Linear Parabolic Partial Differential Equations
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Author : John Christopher Meyer
language : en
Publisher:
Release Date : 2015
The Cauchy Problem For Non Lipschitz Semi Linear Parabolic Partial Differential Equations written by John Christopher Meyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with MATHEMATICS categories.
Theory And Applications Of Abstract Semilinear Cauchy Problems
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Author : Pierre Magal
language : en
Publisher: Springer
Release Date : 2018-11-21
Theory And Applications Of Abstract Semilinear Cauchy Problems written by Pierre Magal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-21 with Mathematics categories.
Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems.
Reaction Diffusion Equations And Their Applications And Computational Aspects Proceedings Of The China Japan Symposium
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Author : Tatsien Li
language : en
Publisher: World Scientific
Release Date : 1997-02-03
Reaction Diffusion Equations And Their Applications And Computational Aspects Proceedings Of The China Japan Symposium written by Tatsien Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-03 with categories.
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.
Estimating The Error Of Numerical Solutions Of Systems Of Reaction Diffusion Equations
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Author : Donald J. Estep
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Estimating The Error Of Numerical Solutions Of Systems Of Reaction Diffusion Equations written by Donald J. Estep 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 2000 with Mathematics categories.
This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the introduction of stability factors, which measure the sensitivity of solutions to various kinds of perturbations. Next, we perform some general analysis on the residual errors and stability factors to determine when they are defined and to bound their size. Then we describe the practical use of the theory to estimate the errors of numerical solutions computationally. Several key issues arise in the implementation that remain unresolved and we present partial results and numerical experiments about these points. We use this approach to estimate the error of numerical solutions of nine standard reaction-diffusion models and make a systematic comparison of the time scale over which accurate numerical solutions can be computed for these problems. We also perform a numerical test of the accuracy and reliability of the computational error estimate using the bistable equation. Finally, we apply the general theory to the class of problems that admit invariant regions for the solutions, which includes seven of the main examples. Under this additional stability assumption, we obtain a convergence result in the form of an upper bound on the error from the a posteriori error estimate. We conclude by discussing the preservation of invariant regions under discretization.
Degenerate Diffusions
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Author : Panagiota Daskalopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2007
Degenerate Diffusions written by Panagiota Daskalopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The book deals with the existence, uniqueness, regularity, and asymptotic behavior of solutions to the initial value problem (Cauchy problem) and the initial-Dirichlet problem for a class of degenerate diffusions modeled on the porous medium type equation $u_t = \Delta u^m$, $m \geq 0$, $u \geq 0$. Such models arise in plasma physics, diffusion through porous media, thin liquid film dynamics, as well as in geometric flows such as the Ricci flow on surfaces and the Yamabe flow. The approach presented to these problems uses local regularity estimates and Harnack type inequalities, which yield compactness for families of solutions. The theory is quite complete in the slow diffusion case ($ m>1$) and in the supercritical fast diffusion case ($m_c