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# A8: Analysis of discretization methods for nonlinear evolution equations

**Principal investigator:**

Prof. Dr. Etienne Emmrich**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.