We discuss possible extensions of the recently established theory of evolutionary Γ-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 Γ-limit approaches based on the energy-dissipation principle or the evolutionary variational estimate.
CITATION STYLE
Mielke, A. (2016). Deriving effective models for multiscale systems via evolutionary Γ -convergence. In Understanding Complex Systems (Vol. 0, pp. 235–251). Springer Verlag. https://doi.org/10.1007/978-3-319-28028-8_12
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