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Research

Major challenges:


For the analysis and numerical analysis of non-smooth non-convex functionals we cannot rely on techniques involving e.g. lower-semi-continuity or reflexivity of Banach spaces. For the algorithmic realization of problems involving Lp functionals, with p∈ (0,1), or truncated Lp functionals with p > 0, we cannot rely on currently available techniques. The dynamical systems behavior of the bidomain equations, a singular reaction-diffusion system coupled with ordinary differential equations, is tremendously rich. Even after model reduction, solving the HJB equation related to optimal control of PDEs remains challenging.

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