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arXiv · 1908.00306

Optimal control of stochastic phase-field models related to tumor growth

Carlo Orrieri·Elisabetta Rocca·Luca Scarpa
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Abstract

We study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion equation governing the nutrient proportion. We prove strong well-posedness of the system in a general framework through monotonicity and stochastic compactness arguments. We introduce then suitable controls representing the concentration of cytotoxic drugs administered in medical treatment and we analyze a related optimal control problem. We derive existence of an optimal strategy and deduce first-order necessary optimality conditions by studying the corresponding linearized system and the backward adjoint system.

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Carlo Orrieri, Elisabetta Rocca, Luca Scarpa. 2019-08-01. Optimal control of stochastic phase-field models related to tumor growth. https://doi.org/10.1051/cocv%2F2020022

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