5 papers · 1 filter
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…
Hyperbolic relaxation of the chemical potential in the viscous Cahn-Hilliard equation
Pierluigi Colli, Jürgen Sprekels
In this paper, we study a hyperbolic relaxation of the viscous Cahn--Hilliard system with zero Neumann boundary conditions. In fact, we consider a relaxation term involving the sec…
Solvability and optimal control of a multi-species Cahn-Hilliard-Keller-Segel tumor growth model
Pierluigi Colli, Gianni Gilardi, Andrea Signori +1
This paper investigates an optimal control problem associated with a two-dimensional multi-species Cahn-Hilliard-Keller-Segel tumor growth model, which incorporates complex biologi…
Curvature effects in pattern formation: well-posedness and optimal control of a sixth-order Cahn-Hilliard equation
Pierluigi Colli, Gianni Gilardi, Andrea Signori +1
This work investigates the well-posedness and optimal control of a sixth-order Cahn-Hilliard equation, a higher-order variant of the celebrated and well-established Cahn-Hilliard e…