Nonlinear evolution equations: model hierarchies and complex fluids (A08)

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Nonlinear evolution equations are the mathematical models for time-dependent processes in science and engineering. We focus on models enriched by, e.g., nonlocality in time or space as well as on non-standard assumptions as, e.g., non-monotone growth. We study existence of generalized solutions via convergence of suitable approximation schemes. Applications arise in soft matter and dynamics of complex fluids. We aim to study models for smectic phases as well as nonlocal models of liquid crystals and to apply the new concept of relative energy.