Parameter Identification via Optimal Control for a Cahn–Hilliard-Chemotaxis System with a Variable Mobility

Christian Kahle, Kei Fong Lam

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

We consider the inverse problem of identifying parameters in a variant of the diffuse interface model for tumour growth proposed by Garcke et al. (Math Models Methods Appl Sci 26(6):1095–1148, 2016). The model contains three constant parameters; namely the tumour growth rate, the chemotaxis parameter and the nutrient consumption rate. We study the inverse problem from the viewpoint of PDE-constrained optimal control theory and establish first order optimality conditions. A chief difficulty in the theoretical analysis lies in proving high order continuous dependence of the strong solutions on the parameters, in order to show the solution map is continuously Fréchet differentiable when the model has a variable mobility. Due to technical restrictions, our results hold only in two dimensions for sufficiently smooth domains. Analogous results for polygonal domains are also shown for the case of constant mobilities. Finally, we propose a discrete scheme for the numerical simulation of the tumour model and solve the inverse problem using a trust-region Gauss–Newton approach.
Original languageEnglish
Pages (from-to)63-104
Number of pages42
JournalApplied Mathematics and Optimization
Volume82
DOIs
Publication statusPublished - Aug 2020

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