Variational Convergence and Stochastic Homogenization of Nonlinear Reaction-Diffusion Problems

Omar Anza Hafsa, Jean-Philippe Mandallena, Gerard Michaille

ISBN 10: 9811258481 / ISBN 13: 9789811258480

Published by World Scientific Pub Co Inc, 2022

About this Item

: Este libro aborda problemas en física, química y biología modelados mediante ecuaciones de reacción-difusión para describir la distribución de temperatura o la concentración de sustancias químicas. También se aplica a problemas de ecología, sociología o dinámica de poblaciones, describiendo la densidad de poblaciones o especies. El libro se centra en la convergencia de secuencias de problemas de Cauchy y su aplicación a situaciones con heterogeneidades espaciales aleatorias. Los problemas límite se ilustran a través de modelos biológicos de invasión y modelos presa-depredador, proporcionando descripciones en términos de ecuaciones de reacción-difusión deterministas y homogéneas. EAN: 9789811258480 Tipo: Libros Categoría: Ciencias|Tecnología|Educación Título: Variational Convergence and Stochastic Homogenization of Nonlinear Reaction-Diffusion Problems Autor: Omar Anza Hafsa| Jean-Philippe Mandallena| Gerard Michaille Editorial: WSPC Idioma: en Páginas: 320 Formato: tapa dura. Seller Inventory # Happ-2024-05-27-84b4a621

Bibliographic Details

Title: Variational Convergence and Stochastic ...

Publisher: World Scientific Pub Co Inc

Publication Date: 2022

Binding: Hardcover

Condition: Como nuevo

About this title

Synopsis:

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.