Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homo\-genization.
The authors deal with the reaction-diffusion system in spatially non-homogeneous almost-periodic media. The vector valued function \(\vec u\) satisfies the differential system \(\partial_t {\vec u} = A_\varepsilon {\vec u} - f({\vec u}) + g\), \({\vec u}| _{\partial \Omega} = 0\). With natural assumptions on the nonlinear term \(f({\vec u})\), the long-time behavior of solutions \({\vec u}\) can be described in terms of the global attractor \({\mathcal A}^\varepsilon\) of the associated dynamical system and that the attractors \({\mathcal A}^\varepsilon\) converge to the attractor \({\mathcal A}^0\) of the homogenized problem as \(\varepsilon \rightarrow 0\). Moreover in the case of periodic media, explicit estimates are given for the distance between the non-homogenized \({\mathcal A}^\varepsilon\) and the homogenized \({\mathcal A}^0\) attractors in terms of the parameter \(\varepsilon\).
scientific article; zbMATH DE number 1881304