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A5: Pattern formation in coupled parabolic systems

Principal investigator:

Prof. Dr. Alexander Mielke [1]

Project summary:

This project studies pattern formation in reaction-diffusion systems and in models of fluid dynamics,
such as Kolmogorov’s two-equation model for turbulence. In addition to traveling waves, such as fronts
and pulses, we also study self-similar structures that describe the asymptotic decay of localized profiles
on unbounded domains. On the methodological side we use homogenization techniques for periodically
structured materials and evolutionary Gamma-convergence for perturbed gradient flows, which will be
combined with self-similar scaling techniques.

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