A5: Pattern formation in systems with multiple scales

Principal investigator:

Prof. Dr. Alexander Mielke [1]

Summary:

Pattern formation in nonlinear partial differential equations depends on nontrivial interactions between
different internal length scales and nonlinearities of the system as well as on the size and geometry
of the underlying domain. The challenge is to understand how effects on the small scales generate
effective pattern formation on the larger 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.