A8: Nonlinear evolution equations: analysis, discretization, and feedback control

Principal investigator:

Prof. Dr. Etienne Emmrich [1]

Summary:

Nonlinear evolution equations are the mathematical models for time-dependent processes in science and
engineering. Relying upon the theory of monotone operators and compactness arguments, we study
existence of solutions, convergence of discretization methods, and feedback control for equations of
dissipative type. We focus on nonlocality in time (distributed delay, memory effects) and interpret time-
delayed feedback control as a nonlocal-in-time coupling. Applications arise in soft matter and dynamics
of complex fluids such as liquid crystals.