86 citations · 451 across the 95 of their papers we have counts for
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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…
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…
Asymptotic analysis of the Allen-Cahn equation with dynamic boundary conditions of Cahn-Hilliard type
Pierluigi Colli, Takeshi Fukao
Problems for partial differential equations coupled with dynamic boundary conditions can be viewed as a type of transmission problem between the bulk and its boundary. For the heat…
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…
Hyperbolic relaxation of a sixth-order Cahn-Hilliard equation
Pierluigi Colli, Gianni Gilardi
This work explores the solvability of a sixth-order Cahn--Hilliard equation with an inertial term, which serves as a relaxation of a higher-order variant of the classical Cahn--Hil…
On the optimal control of viscous Cahn-Hilliard systems with hyperbolic relaxation of the chemical potential
Pierluigi Colli, Jürgen Sprekels
In this paper, we study an optimal control problem for a viscous Cahn--Hilliard system with zero Neumann boundary conditions in which a hyperbolic relaxation term involving the sec…