Identification of a chemotactic sensitivity in a coupled system

TL;DR

This paper develops methods to identify chemotactic sensitivities in biological systems from experimental data, accounting for nonlinear dependencies, and provides theoretical and numerical analysis of the inverse problem.

Contribution

It introduces a framework for recovering nonlinear chemotactic sensitivities using inverse problem techniques and Tikhonov regularization, with convergence analysis and numerical validation.

Findings

Existence of solutions to the forward problem established.

Convergence of the regularization method demonstrated.

Numerical experiments confirm the approach's effectiveness.

Abstract

Chemotaxis is the process by which cells behave in a way that follows the chemical gradient. Applications to bacteria growth, tissue inflammation, and vascular tumors provide a focus on optimization strategies. Experiments can characterize the form of possible chemotactic sensitivities. This paper addresses the recovery of the chemotactic sensitivity from these experiments while allowing for nonlinear dependence of the parameter on the state variables. The existence of solutions to the forward problem is analyzed. The identification of a chemotactic parameter is determined by inverse problem techniques. Tikhonov regularization is investigated and appropriate convergence results are obtained. Numerical results of concentration dependent chemotactic terms are explored.