1 citations · 2 across the 9 of their papers we have counts for
13 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…
Global existence for Consensus-Based Kinetic Models for Image Segmentation
Abramo Agosti, Pierluigi Colli, Elisabetta Rocca +1
In this article, we analyze a recently introduced kinetic model based on Hegselmann-Krause-type interaction dynamics describing consensus-based image segmentation in the mean-field…
Optimal control for a fourth-order nonisothermal tumor growth model of Caginalp type
Giulia Cavalleri, Pierluigi Colli, Elisabetta Rocca
We study a distributed optimal control problem for a nonisothermal Caginalp-type phase-field model that describes tumour growth under thermal therapy. The PDE system couples a poss…
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…
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 a Brain Tumor Growth Model with Lactate Metabolism, Viscoelastic Effects, and Tissue Damage
Giulia Cavalleri, Pierluigi Colli, Alain Miranville +1
In this paper, we study a nonlinearly coupled initial-boundary value problem describing the evolution of brain tumor growth including lactate metabolism. In our modeling approach,…
Chemotaxis-inspired PDE model for airborne infectious disease transmission: analysis and simulations
Pierluigi Colli, Gabriela Marinoschi, Elisabetta Rocca +1
Partial differential equation (PDE) models for infectious disease have received renewed interest in recent years. Most models of this type extend classical compartmental formulatio…
A rigorous approach to the sharp interface limit for phase-field models of tumor growth
Filippo Riva, Elisabetta Rocca
In this paper we consider two diffuse interface models for tumor growth coupling a Cahn-Hilliard type equation for the tumor phase parameter to a reaction-diffusion type equation f…
Local asymptotics and optimal control for a viscous Cahn-Hilliard-Reaction-Diffusion model for tumor growth
Elisa Davoli, Elisabetta Rocca, Luca Scarpa +1
In this paper we study nonlocal-to-local asymptotics for a tumor-growth model coupling a viscous Cahn-Hilliard equation describing the tumor proportion with a reaction-diffusion eq…
Periodic waves in unsaturated porous media with hysteresis
B. Albers, P. Krejci, E. Rocca
We consider a PDE system with degenerate hysteresis describing unsaturated flow in 3D porous media. Assuming that a time periodic forcing is prescribed on the boundary, we prove th…
Sharp interface control in a Penrose-Fife model
Pierluigi Colli, Gabriela Marinoschi, Elisabetta Rocca
In this paper we study a singular control problem for a system of PDEs describing a phase-field model of Penrose-Fife type. The main novelty of this contribution consists in the id…
Analysis and simulations of multifrequency induction hardening
D. Hoemberg, T. Petzold, E. Rocca
We study a model for induction hardening of steel. The related differential system consists of a time domain vector potential formulation of the Maxwell's equations coupled with an…