Penalisation of Long Treatment Time and Optimal Control of a Tumour Growth Model of Cahn-Hilliard

Abstract

A distributed optimal control problem for a diffuse interface model, which physical context is that of tumour growth dynamics, is addressed. The system we deal with comprises a Cahn--Hilliard equation for the tumour fraction coupled with a reaction-diffusion for a nutrient species surrounding the tumourous cells. The cost functional to be minimised possesses some objective terms and it also penalises long treatments time, which may affect harm to the patients, and big aggregations of tumourous cells. Hence, the optimisation problem leads to the optimal strategy which reduces the time exposure of the patient to the medication and at the same time allows the doctors to achieve suitable clinical goals.

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Cited by in corpus (2)

• On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport
• Second-order analysis of an optimal control problem in a phase field tumor growth model with singular potentials and chemotaxis