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An inverse problem for a model of cell motion and chemotaxis

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An inverse problem for a model of cell motion and chemotaxis
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19
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The viewpoint proposed in this lecture is that uncertaintyquantification for kinetic equations does not always represent the viewpointof the experimentalists. Instead they want to determine the uncertain co-efficient in a PDE by measuring the solution at the parts of the boundary,given data on other parts of the boundary. In other words experimentalistsare interested in solving the inverse problem in a Baysian setting. We shall give examples and results to this end. In particular we shallconsider a model from mathematical biology, namely the motion of cells, as described by the kinetic chemotaxis equations. The corresponding macro-scopic Keller-Segel type model will be a diffusion equation. Our aim is tostudy the inverse problems for these two settings. We shall analytically studythe convergence of the inverse problem of the kinetic equation to the inverseproblem of the corresponding diffusion equation. This is joint work with Kathrin Hellmuth, Qin Li and Min Tang.