On a nonisothermal tumor growth model of Caginalp type

Giulia Cavalleri (U of Pavia)

Dec 10. 2025, 11:30 — 12:00

We study an optimal control problem for a nonisothermal phase-field system of Caginalp type that describes tumor growth under thermal therapy. The model 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. The resulting nonlinear system incorporates chemotaxis and active transport effects, and hyperthermia appears as a control variable. Well-posedness for the initial-boundary value problem and additional regularity are proven. Then, we define a suitable cost functional and show the existence of optimal controls. Finally, we analyze the differentiability of the control-to-state operator and establish a necessary first-order condition for treatment optimality. These results have been obtained in collaboration with Pierluigi Colli (University of Pavia) and Elisabetta Rocca (University of Pavia).
 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Free Boundary Problems (Thematic Programme)
Organizer(s):
Serena Dipierro (UWA, Perth)
Julian Fischer (ISTA, Klosterneuburg)
Matteo Novaga (U Pisa)
Elisabetta Rocca (U of Pavia)
Xavier Ros-Oton (U of Barcelona)
Ulisse Stefanelli (U of Vienna)
Enrico Valdinoci (UWA, Perth)