11 papers · 1 filter
Permeability parameter asymptotics in a Cahn--Hilliard system with third type transmission conditions
Pierluigi Colli, Takeshi Fukao, Kei Fong Lam
In this paper, we study a system in which the Cahn--Hilliard system is imposed in the bulk domain and an Allen--Cahn type equation is prescribed on the boundary, connected through…
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…
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…
Two-phase flows through porous media described by a Cahn--Hilliard--Brinkman model with dynamic boundary conditions
Pierluigi Colli, Patrik Knopf, Giulio Schimperna +1
We investigate a new diffuse-interface model that describes creeping two-phase flows (i.e., flows exhibiting a low Reynolds number), especially flows that permeate a porous medium.…
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…