Chemotaxis models are typically able to develop blow-up in finite times. For some specific models, we obtain some estimates on the set of concentration of cells (defined roughly as the points where the density of cells is infinite with a non-vanishing mass). More precisely we consider models without diffusion for which the cells' velocity decreases if the concentration of the chemical attractant becomes too large. We are able to give a lower bound on the Hausdorff dimension of the concentration set, one in the "best" situation where the velocity exactly vanishes for too large concentrations of attractant. This in particular implies that the solution may not form any Dirac mass.
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