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.
Funder
Austrian Science Fund
Ministero dell’Istruzione, dell’Università e della Ricerca
Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
Fondazione Cariplo
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
Cited by
12 articles.
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