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Appl Math Optim https://doi.org/10.1007/s00245-018-9491-z Parameter Identification via Optimal Control for a Cahn–Hilliard-Chemotaxis System with a Variable Mobility 1 2 Christian Kahle · Kei Fong Lam © Springer Science+Business Media, LLC, part of Springer Nature 2018 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 con- stant 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 depen- dence 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 con- stant mobilities. Finally, we propose a discrete scheme for the numerical simulation of the tumour model and solve the inverse problem using a trust-region
Applied Mathematics and Optimization – Springer Journals
Published: Mar 22, 2018
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