Optimal control of stochastic phase-field models related to tumor growth
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 104.

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.

DOI : 10.1051/cocv/2020022
Classification : 35R60, 35K55, 49J20, 78A70
Mots-clés : Stochastic systems of partial differential equations, Cahn-Hilliard equation, optimal control, first-order necessary conditions, tumor growth 
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     title = {Optimal control of stochastic phase-field models related to tumor growth},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {26},
     year = {2020},
     doi = {10.1051/cocv/2020022},
     mrnumber = {4185061},
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     url = {http://www.numdam.org/articles/10.1051/cocv/2020022/}
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Orrieri, Carlo; Rocca, Elisabetta; Scarpa, Luca. Optimal control of stochastic phase-field models related to tumor growth. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 104. doi : 10.1051/cocv/2020022. http://www.numdam.org/articles/10.1051/cocv/2020022/

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