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Maximum principle of optimal control of a Cahn–Hilliard–Navier–Stokes model with state constraints
Author(s) -
Tachim Medjo Theodore,
Tone Cristina,
Tone Florentina
Publication year - 2021
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2701
Subject(s) - maximum principle , pontryagin's minimum principle , cahn–hilliard equation , mathematics , optimal control , bounded function , domain (mathematical analysis) , navier–stokes equations , coupling (piping) , state (computer science) , mathematical analysis , mathematical optimization , physics , compressibility , partial differential equation , mechanics , algorithm , mechanical engineering , engineering
We investigate in this article Pontryagin's maximum principle for a class of control problems associated with a Cahn–Hilliard–Navier–Stokes model in a two dimensional bounded domain. The model consists of the Navier–Stokes equations for the velocity v , coupled with a Cahn–Hilliard model for the order (phase) parameter ϕ . We derive Pontryagin's maximum principle for the control problems assuming that a solution exists. Let us note that the coupling between the Navier–Stokes and the Cahn–Hilliard systems makes the analysis of the control problem more involved.