Inserted: 4 may 2020
Last Updated: 4 may 2020
Journal: Math. Methods Appl. Sci.
Sliding mode control - Cahn-Hilliard system - Reaction-diffusion equation - Tumor growth - Nonlinear boundary value problem - State-feedback control law.
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.