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.
Contents:PrefaceIntroductionSequences of Reaction-Diffusion Problems: Convergence:Variational Convergence of Nonlinear Reaction-Diffusion EquationsVariational Convergence of Nonlinear Distributed Time Delays Reaction-Diffusion EquationsVariational Convergence of Two Components Nonlinear Reaction-Diffusion SystemsVariational Convergence of Integrodifferential Reaction-Diffusion EquationsVariational Convergence of a Class of Functionals Indexed by Young MeasuresSequences of Reaction-Diffusion Problems: Stochastic Homogenization:Stochastic Homogenization of Nonlinear Reaction-Diffusion EquationsStochastic Homogenization of Nonlinear Distributed Time Delays Reaction-Diffusion EquationsStochastic Homogenization of Two Components Nonlinear Reaction-Diffusion SystemsStochastic Homogenization of Integrodifferential Reaction-Diffusion EquationsStochastic Homogenization of Non Diffusive Reaction Equations and Memory EffectAppendices:Grönwall Type InequalitiesBasic Notions on Variational ConvergencesErgodic Theory and Subadditive ProcessesLarge Deviations PrincipleMeasure TheoryInf-Convolution and Parallel SumBibliographyNotationIndex
Readership: Graduate students and researchers.