77 citations · 150 across the 27 of their papers we have counts for
44 papers
Asymptotic analysis of an optimal control problem for a phase field tumor growth model with hyperbolic relaxation of the chemical potential
Pierluigi Colli, Elisabetta Rocca, Jürgen Sprekels
In this paper, we study the optimal control of a phase field tumor growth model of Cahn--Hilliard type with possibly singular potential in which the often assumed parabolic relaxat…
Optimal control of a tumor growth model with hyperbolic relaxation of the chemical potential
Pierluigi Colli, Elisabetta Rocca, Jürgen Sprekels
In this paper, we study the optimal control of a phase field model for a tumor growth model of Cahn--Hilliard type in which the often assumed parabolic relaxation of the chemical p…
Optimal velocity control of a Brinkman-Cahn-Hilliard system with curvature effects
Pierluigi Colli, Gianni Gilardi, Andrea Signori +1
We address an optimal control problem governed by a system coupling a Brinkman-type momentum equation for the velocity field with a sixth-order Cahn-Hilliard equation for the phase…
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…
Second-order optimality conditions for the sparse optimal control of nonviscous Cahn-Hilliard systems
Pierluigi Colli, Jürgen Sprekels
In this paper we study the optimal control of an initial-boundary value problem for the classical nonviscous Cahn-Hilliard system with zero Neumann boundary conditions. Phase field…
Optimality conditions for sparse optimal control of viscous Cahn-Hilliard systems with logarithmic potential
Pierluigi Colli, Jürgen Sprekels, Fredi Tröltzsch
In this paper we study the optimal control of a parabolic initial-boundary value problem of viscous Cahn-Hilliard type with zero Neumann boundary conditions. Phase field systems of…
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…
Nutrient control for a viscous Cahn-Hilliard-Keller-Segel model
Gianni Gilardi, Andrea Signori, Jürgen Sprekels
In this paper, we address a distributed control problem for a system of partial differential equations describing the evolution of a tumor that takes the biological mechanism of ch…
Second-order sufficient conditions in the sparse optimal control of a phase field tumor growth model with logarithmic potential
Jürgen Sprekels, Fredi Tröltzsch
This paper treats a distributed optimal control problem for a tumor growth model of viscous Cahn--Hilliard type. The evolution of the tumor fraction is governed by a thermodynamic…
Second-order sufficient conditions for sparse optimal control of singular Allen--Cahn systems with dynamic boundary conditions
Jürgen Sprekels, Fredi Tröltzsch
In this paper we study the optimal control of a parabolic initial-boundary value problem of Allen--Cahn type with dynamic boundary conditions. Phase field systems of this type gove…
Optimal temperature distribution for a nonisothermal Cahn-Hilliard system in two dimensions with source term and double obstacle potential
Pierluigi Colli, Gianni Gilardi, Andrea Signori +1
In this note, we study the optimal control of a nonisothermal phase field system of Cahn-Hilliard type that constitutes an extension of the classical Caginalp model for nonisotherm…
Optimal temperature distribution for a nonisothermal Cahn-Hilliard system with source term
Pierluigi Colli, Gianni Gilardi, Andrea Signori +1
In this note, we study the optimal control of a nonisothermal phase field system of Cahn-Hilliard type that constitutes an extension of the classical Caginalp model for nonisotherm…
Optimal control of a nonconserved phase field model of Caginalp type with thermal memory and double obstacle potential
Pierluigi Colli, Gianni Gilardi, Andrea Signori +1
In this paper, we investigate optimal control problems for a nonlinear state system which constitutes a version of the Caginalp phase field system modeling nonisothermal phase tran…
On a Cahn-Hilliard system with source term and thermal memory
Pierluigi Colli, Gianni Gilardi, Andrea Signori +1
A nonisothermal phase field system of Cahn-Hilliard type is introduced and analyzed mathematically. The system constitutes an extension of the classical Caginalp model for nonisoth…
Cahn-Hilliard-Brinkman model for tumor growth with possibly singular potentials
Pierluigi Colli, Gianni Gilardi, Andrea Signori +1
We analyze a phase field model for tumor growth consisting of a Cahn-Hilliard-Brinkman system, ruling the evolution of the tumor mass, coupled with an advection-reaction-diffusion…
Well-posedness and optimal control for a Cahn-Hilliard-Oono system with control in the mass term
Pierluigi Colli, Gianni Gilardi, Elisabetta Rocca +1
The paper treats the problem of optimal distributed control of a Cahn-Hilliard-Oono system in , , with the control located in the mass term and admitti…
Second-order analysis of an optimal control problem in a phase field tumor growth model with singular potentials and chemotaxis
Pierluigi Colli, Andrea Signori, Jürgen Sprekels
This paper concerns a distributed optimal control problem for a tumor growth model of Cahn-Hilliard type including chemotaxis with possibly singular potentials, where the control a…
An asymptotic analysis for a generalized Cahn-Hilliard system with fractional operators
Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels
In the recent paper `Well-posedness and regularity for a generalized fractional Cahn-Hilliard system' (Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), 437-478 -- see als…
Asymptotic analysis of a tumor growth model with fractional operators
Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels
In this paper, we study a system of three evolutionary operator equations involving fractional powers of selfadjoint, monotone, unbounded, linear operators having compact resolvent…
A distributed control problem for a fractional tumor growth model
Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels
In this paper, the authors study the distributed optimal control of a system of three evolutionary equations involving fractional powers of three selfadjoint, monotone, unbounded l…
Optimal control of a phase field system modelling tumor growth with chemotaxis and singular potentials
Pierluigi Colli, Andrea Signori, Jürgen Sprekels
A distributed optimal control problem for an extended model of phase field type for tumor growth is addressed. In this model, the chemotaxis effects are also taken into account. Th…
Optimal distributed control of a generalized fractional Cahn-Hilliard system
Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels
In the recent paper `Well-posedness and regularity for a generalized fractional Cahn-Hilliard system' (arXiv:1804.11290) by the same authors, general well-posedness results have be…