Sliding mode control for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation |
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Authors: | Michele Colturato |
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Institution: | Dipartimento di Medicina Molecolare e Transazionale, Università degli Studi di Brescia, Brescia, Italy |
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Abstract: | 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. |
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Keywords: | Cahn–Hilliard system nonlinear boundary value problem reaction–diffusion equation sliding mode control state-feedback control law tumor growth |
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