Inverse Problems for Drift-Diffusion Equations with Applications to Chemotaxis and Synthetic Nanopores

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In this renewal proposal we consider questions related to inverse problems of nonlinear drift--diffusion equations and systems thereof. One focus is the treatment of chemotaxis, defined as the directed movement of cells along the gradient of a chemical substance. This is modelled by equations featuring unknown nonlinear functions which we aim to reconstruct given measurements of the cell density. We also treat the problem of stable reconstruction of these functions and the analysis of numerical schemes which allow the application to real data. An additional aspect is the treatment of lower order terms as well as the usage of nonlinear boundary conditions. Finally, we consider the modelling, simulation and optimisation of synthetic nanopores.