Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction-diffusion Problems
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A01=Gerard Michaille
A01=Jean-philippe Mandallena
A01=Omar Anza Hafsa
Author_Gerard Michaille
Author_Jean-philippe Mandallena
Author_Omar Anza Hafsa
Category=PBKJ
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Gamma Convergence
Integrodifferential Reaction-Diffusion Equations
Memory Effect
Population Dynamics
Prey-Predator Random Models
Reaction-Diffusion Equations or Systems
Stochastic Homogenization
Time Delays Reaction-Diffusion Equations
Product details
- ISBN 9789811258480
- Publication Date: 20 Jul 2022
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
