Sparse optimal control of a phase field tumour model with mechanical effects

Abstract

In this paper, we study an optimal control problem for a macroscopic mechanical tumour model based on the phase field approach. The model couples a Cahn--Hilliard type equation to a system of linear elasticity and a reaction-diffusion equation for a nutrient concentration. By taking advantage of previous analytical well-posedness results established by the authors, we seek optimal controls in the form of a boundary nutrient supply, as well as concentrations of cytotoxic and antiangiogenic drugs that minimise a cost functional involving mechanical stresses. Special attention is given to sparsity effects, where with the inclusion of convex non-differentiable regularisation terms to the cost functional, we can infer from the first-order optimality conditions that the optimal drug concentrations can vanish on certain time intervals.

arXiv comment26 pages

References in corpus (4)

• A coupled surface-Cahn--Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes
• Long-time Dynamics and Optimal Control of a Diffuse Interface Model for Tumor Growth
• On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects
• Strong well-posedness and inverse identification problem of a non-local phase field tumor model with degenerate mobilities

Cited by in corpus (4)

• Viscoelastic Cahn--Hilliard models for tumour growth
• A phase field model of Cahn-Hilliard type for tumour growth with mechanical effects and damage
• Existence of weak solutions to multiphase Cahn-Hilliard-Darcy and Cahn-Hilliard-Brinkman models for stratified tumor growth with chemotaxis and general source terms
• Optimal control problems with sparsity for phase field tumor growth models involving variational inequalities