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Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction-diffusion Problems (Hardcover)
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Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction-diffusion Problems (Hardcover)
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Total price: R2,932
Discovery Miles: 29 320
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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 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.
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