9 papers · 1 filter
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…
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…
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…