2019/08/01 by Carlo Orrieri, Elisabetta Rocca, Luca Scarpa · 16 citations
Engineering · Materials Science · Mathematics · #Compact space #Coupling (piping) #Mathematical Biology Tumor Growth #Monotonic function #Optimal control #Piezoelectric Actuators and Control #Solidification and crystal growth phenomena #Stochastic control #Stochastic modelling #Stochastic process #math.AP #math.OC #math.PR #msc:35K55 #msc:35R60 #msc:49J20 #msc:78A70
paper · pdf · doi:10.1051/cocv/2020022
published in ESAIM Control Optimisation and Calculus of Variations 26, 104 (EDP Sciences) · 39 pages
arxiv created 2019/08/01 · openalex created_date 2019/08/13 · openalex publication_date 2020/01/01 · arxiv updated 2021/01/19 · openalex updated_date 2026/08/05
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.