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math.AP2026
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…
math.AP2025
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…
math.AP2025
On a Brain Tumor Growth Model with Lactate Metabolism, Viscoelastic Effects, and Tissue Damage
Giulia Cavalleri, Pierluigi Colli, Alain Miranville +1
In this paper, we study a nonlinearly coupled initial-boundary value problem describing the evolution of brain tumor growth including lactate metabolism. In our modeling approach,…