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

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.

arXiv comment39 pages

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Cited by in corpus (5)

• Modeling and simulation of vascular tumors embedded in evolving capillary networks
• On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport
• Stochastic maximum principle for problems with delay with general dependence on the past
• Analysis and optimal velocity control of a stochastic convective Cahn-Hilliard equation
• The stochastic Cahn-Hilliard equation with degenerate mobility and logarithmic potential