scholarly journals Sparse Optimal Control of a Phase Field Tumor Model with Mechanical Effects

2021 ◽  
Vol 59 (2) ◽  
pp. 1555-1580
Author(s):  
Harald Garcke ◽  
Kei Fong Lam ◽  
Andrea Signori
Keyword(s):  
Optimal Control ◽  
Phase Field ◽  
Tumor Model ◽  
Mechanical Effects ◽  
Sparse Optimal Control

scholarly journals Distributed optimal control of a nonstandard nonlocal phase field system

2016 ◽  
Vol 1 (3) ◽  
pp. 225-260 ◽  
Author(s):  
Pierluigi Colli ◽  
◽  
Gianni Gilardi ◽  
Jürgen Sprekels
Keyword(s):  
Optimal Control ◽  
Phase Field ◽  
Distributed Optimal Control ◽  
Field System ◽  
Phase Field System

scholarly journals Optimal control of stochastic phase-field models related to tumor growth

2020 ◽  
Vol 26 ◽  
pp. 104
Author(s):  
Carlo Orrieri ◽  
Elisabetta Rocca ◽  
Luca Scarpa
Keyword(s):  
Optimal Control ◽  
Tumor Growth ◽  
Phase Field ◽  
Phase Field Model ◽  
Growth Dynamics ◽  
Necessary Optimality Conditions ◽  
Reaction Diffusion ◽  
Adjoint System ◽  
Reaction Diffusion Equation ◽  
Cahn Hilliard Equation

We study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion equation governing the nutrient proportion. We prove strong well-posedness of the system in a general framework through monotonicity and stochastic compactness arguments. We introduce then suitable controls representing the concentration of cytotoxic drugs administered in medical treatment and we analyze a related optimal control problem. We derive existence of an optimal strategy and deduce first-order necessary optimality conditions by studying the corresponding linearized system and the backward adjoint system.

scholarly journals Distributed optimal control of a nonstandard system of phase field equations

2011 ◽  
Vol 24 (4-6) ◽  
pp. 437-459 ◽  
Author(s):  
Pierluigi Colli ◽  
Gianni Gilardi ◽  
Paolo Podio-Guidugli ◽  
Jürgen Sprekels
Keyword(s):  
Optimal Control ◽  
Phase Field ◽  
Field Equations ◽  
Distributed Optimal Control ◽  
Phase Field Equations
Sign in / Sign up

Export Citation Format

Share Document