Journal Article

Identification of a chemotactic sensitivity in a coupled system

K. Renee Fister and Maeve L. McCarthy

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 25, issue 3, pages 215-232
Published in print September 2008 | ISSN: 1477-8599
Published online July 2008 | e-ISSN: 1477-8602 | DOI: https://dx.doi.org/10.1093/imammb/dqn015
Identification of a chemotactic sensitivity in a coupled system

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Chemotaxis is the process by which cells behave in a way that follows the chemical gradient. Applications to bacteria growth, tissue inflammation and vascular tumours 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 non-linear dependence of the parameter on the state variables. The existence of solutions to the forward problem is analysed. 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.

Keywords: inverse problem; chemotaxis; Tikhonov regularization

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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