### Inhalt des Dokuments

# A8: Analysis of discretization methods for nonlinear evolution equations

**Principal investigator:**

Prof. Dr. Etienne Emmrich [1]**Project summary:**The mathematical modeling of time-dependent processes
in science and engineering leads to, in general, nonlinear evolution
equations of first or second order in time. The highest spatial
derivatives appearing can often be described by a monotone and
coercive operator; lower order terms are then treated as a strongly
continuous perturbation of the principal part. Relying upon the
variational approach and the theory of monotone operators, the
approximate solution of such evolution problems is studied with focus
on problems with nonlocality in time and on the convergence of
appropriate discretization methods. Applications arise in the
description of complex fluids as well as of neuron dynamics. A long
term goal is the question of controllability of the systems
above.