Volume 26, 2020
|Number of page(s)||46|
|Published online||10 December 2020|
Optimal control of stochastic phase-field models related to tumor growth
Department of Mathematics, University of Trento Via Sommarive 14,
Povo (Trento), Italy.
2 Department of Mathematics, University of Pavia, and IMATI - C.N.R. Via Ferrata 5, 27100 Pavia, Italy.
3 Faculty of Mathematics, University of Vienna Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
* Corresponding author: firstname.lastname@example.org
Accepted: 23 April 2020
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.
Mathematics Subject Classification: 35R60 / 35K55 / 49J20 / 78A70
Key words: Stochastic systems of partial differential equations / Cahn-Hilliard equation / optimal control, first-order necessary conditions / tumor growth
© EDP Sciences, SMAI 2020
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