A5: Pattern formation in coupled parabolic systems

Principal investigator:

Prof. Dr. Alexander Mielke

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.