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

Parameter Identification via Optimal Control for a Cahn–Hilliard-Chemotaxis System with a... 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

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

Kahle, Christian; Lam, Kei
Applied Mathematics and Optimization , Volume OnlineFirst – Mar 22, 2018
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References (36)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-018-9491-z
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Mar 22, 2018

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