33 citations · 162 across the 26 of their papers we have counts for
27 papers
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 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…
Optimal Control of a Navier-Stokes-Cahn-Hilliard System for Membrane-fluid Interaction
Andrea Signori, Hao Wu
We consider an optimal control problem for a two-dimensional Navier-Stokes-Cahn-Hilliard system arising in the modeling of fluid-membrane interaction. The fluid dynamics is governe…
On a Cahn-Hilliard equation for the growth and division of chemically active droplets modeling protocells
Harald Garcke, Kei Fong Lam, Robert Nürnberg +1
The Cahn-Hilliard model with reaction terms can lead to situations in which no coarsening is taking place and, in contrast, growth and division of droplets occur which all do not g…
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…
Well-posedness and optimal control for a viscous Cahn-Hilliard-Oono system with dynamic boundary conditions
Gianni Gilardi, Elisabetta Rocca, Andrea Signori
In this paper we consider a nonlinear system of PDEs coupling the viscous Cahn-Hilliard-Oono equation with dynamic boundary conditions enjoying a similar structure on the boundary.…
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…
Regularity results and optimal velocity control of the convective nonlocal Cahn-Hilliard equation in 3D
Andrea Poiatti, Andrea Signori
In this contribution, we study an optimal control problem for the celebrated nonlocal Cahn-Hilliard equation endowed with the singular Flory-Huggins potential in the three-dimensio…
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…
Analysis and optimal control theory for a phase field model of Caginalp type with thermal memory
Pierluigi Colli, Andrea Signori, Jürgen Sprekels
A nonlinear extension of the Caginalp phase field system is considered that takes thermal memory into account. The resulting model, which is a first-order approximation of a thermo…
Existence of weak solutions to multiphase Cahn-Hilliard-Darcy and Cahn-Hilliard-Brinkman models for stratified tumor growth with chemotaxis and general source terms
Patrik Knopf, Andrea Signori
We investigate a multiphase Cahn-Hilliard model for tumor growth with general source terms. The multiphase approach allows us to consider multiple cell types and multiple chemical…
Optimal control problems with sparsity for phase field tumor growth models involving variational inequalities
Pierluigi Colli, Andrea Signori, Jürgen Sprekels
This paper treats a distributed optimal control problem for a tumor growth model of Cahn-Hilliard type including chemotaxis. The evolution of the tumor fraction is governed by a va…
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…
Strong well-posedness and inverse identification problem of a non-local phase field tumor model with degenerate mobilities
S. Frigeri, K. F. Lam, A. Signori
We extend previous weak well-posedness results obtained in Frigeri et al. (2017) concerning a non-local variant of a diffuse interface tumor model proposed by Hawkins-Daarud et al.…
On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport
Luca Scarpa, Andrea Signori
This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. Thes…
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…
Penalisation of Long Treatment Time and Optimal Control of a Tumour Growth Model of Cahn-Hilliard
Andrea Signori
A distributed optimal control problem for a diffuse interface model, which physical context is that of tumour growth dynamics, is addressed. The system we deal with comprises a Cah…
Boundary control problem and optimality conditions for the Cahn-Hilliard equation with dynamic boundary conditions
Pierluigi Colli, Andrea Signori
This paper is concerned with a boundary control problem for the Cahn--Hilliard equation coupled with dynamic boundary conditions. In order to handle the control problem, we restric…
Vanishing parameter for an optimal control problem modeling tumor growth
Andrea Signori
A distributed optimal control problem for a phase field system which physical context is that of tumor growth is discussed. The system we are going to take into account consists of…