Identification of Chemotaxis Models with Volume Filling

TL;DR

This paper addresses the inverse problem of identifying nonlinear chemotactic sensitivity and chemoattractant production functions in a volume filling chemotaxis model, employing Tikhonov regularization and supporting findings with numerical tests.

Contribution

It introduces a method for identifying key nonlinear functions in chemotaxis models with volume filling, including a numerical regularization approach.

Findings

Successful numerical implementation of Tikhonov regularization

Stable reconstruction of nonlinear functions demonstrated

Theoretical analysis supports numerical results

Abstract

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 non-linear 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.