Identification of Chemotaxis Models with Volume-Filling

Chemotaxis refers to the directed movement of cells in response to a chemical signal called chemoattractant. A crucial point in the mathematical modeling of chemotactic processes is the correct description of the chemotactic sensitivity and of the production rate of the chemoattractant. In this paper, we investigate the identification of these nonlinear parameter functions in a chemotaxis model with volume-filling. We also discuss the numerical realization of Tikhonov regularization for the stable solution of the inverse problem. Our theoretical findings are supported by numerical tests.