Optimal control for a fourth-order nonisothermal tumor growth model of Caginalp type
Abstract
We study a distributed optimal control problem for a nonisothermal Caginalp-type phase-field model that describes tumour growth under thermal therapy. The PDE system couples a possibly viscous Cahn-Hilliard equation, governing the evolution of the healthy and tumor phases, with an equation for the heat balance, and a reaction-diffusion equation for the nutrient concentration. Chemotaxis and active transport effects are taken into account, and hyperthermia appears as a control variable. We introduce a suitable tracking-type cost functional and show the existence of optimal controls. Then, we analyse the differentiability of the control-to-state operator and establish necessary first-order conditions expressed through a variational inequality involving the adjoint state variables.
Cite
@article{arxiv.2604.24108,
title = {Optimal control for a fourth-order nonisothermal tumor growth model of Caginalp type},
author = {Giulia Cavalleri and Pierluigi Colli and Elisabetta Rocca},
journal= {arXiv preprint arXiv:2604.24108},
year = {2026}
}
Comments
35 pages. The keywords are: tumor growth model, Cahn--Hilliard system, nonisothermal model, optimal control, adjoint system, necessary optimality conditions