13 papers
Optimal control for a fourth-order nonisothermal tumor growth model of Caginalp type
Giulia Cavalleri, Pierluigi Colli, Elisabetta Rocca
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 poss…
Optimal control of a tumor growth model with hyperbolic relaxation of the chemical potential
Pierluigi Colli, Elisabetta Rocca, Jürgen Sprekels
In this paper, we study the optimal control of a phase field model for a tumor growth model of Cahn--Hilliard type in which the often assumed parabolic relaxation of the chemical p…
On the hyperbolic relaxation of the chemical potential in a phase field tumor growth model
Pierluigi Colli, Elisabetta Rocca, Jürgen Sprekels
In this paper, we study a phase field model for a tumor growth model of Cahn--Hilliard type in which the often assumed parabolic relaxation of the chemical potential is replaced by…
Optimal velocity control of a Brinkman-Cahn-Hilliard system with curvature effects
Pierluigi Colli, Gianni Gilardi, Andrea Signori +1
We address an optimal control problem governed by a system coupling a Brinkman-type momentum equation for the velocity field with a sixth-order Cahn-Hilliard equation for the phase…
Well-posedness for a fourth-order nonisothermal tumor growth model of Caginalp type
Giulia Cavalleri, Pierluigi Colli, Elisabetta Rocca
We introduce a nonisothermal phase-field system of Caginalp type that describes tumor growth under hyperthermia. The model couples a possibly viscous Cahn-Hilliard equation, govern…
On Brinkman flows with curvature-induced phase separation in binary mixtures
Pierluigi Colli, Gianni Gilardi, Andrea Signori +1
The mathematical analysis of diffuse-interface models for multiphase flows has attracted significant attention due to their ability to capture complex interfacial dynamics, includi…