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Sliding mode control for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation
Author(s) -
Colturato Michele
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6403
Subject(s) - cahn–hilliard equation , uniqueness , mathematics , monotone polygon , diffusion equation , diffusion , coupling (piping) , constant (computer programming) , mathematical analysis , allen–cahn equation , manifold (fluid mechanics) , nonlinear system , partial differential equation , geometry , physics , materials science , thermodynamics , economy , economics , service (business) , mechanical engineering , quantum mechanics , computer science , metallurgy , engineering , programming language
We consider the sliding mode control (SMC) problem for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation perturbed by a maximal monotone nonlinearity. We prove existence and regularity of strong solutions and, under further assumptions, a uniqueness result. Then, we show that the chosen SMC law forces the system to reach within finite time a sliding manifold that we chose in order that the tumor phase remains constant in time.