A5: Pattern formation in systems with multiple scales

Principal investigator:

Prof. Dr. Alexander Mielke

Project summary:

Pattern formation in nonlinear partial differential equations depends on nontrivial interactions between different internal length scales of the system, the nonlinearities and the size and geometry of the underlying domain.  The challenge is to understand how effects on the small spatial scales generate effective pattern formation on large spatial scales. Using well-chosen model problems reflecting the focus applications of the CRC, we will investigate the mathematical foundations of the derivation of effective models for pattern formation in multiscale problems. Controls for the effective models will be used to construct controls for the original system.