(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Mielke, Alexander
We discuss possible extensions of the recently established theory of
evolutionary Gamma-convergence for gradient systems to nonlinear dynamical
systems obtained by perturbation of a gradient systems. Thus, it is possible
to derive effective equations for pattern forming systems with multiple
scales. Our applications include homogenization of reaction-diffusion
systems, the justification of amplitude equations for Turing instabilities,
and the limit from pure diffusion to reaction-diffusion. This is achieved by
generalizing the Gamma-limit approaches based on the energy-dissipation
principle or the volutionary variational estimate.
