We consider the heat equation with dynamic boundary conditions involving gradient terms in a bounded domain. In this paper we study the cost of approximate controllability for this equation. Combining new developed Carleman estimates and some optimization techniques, we obtain explicit bounds of the minimal norm control. We consider the linear and the semilinear cases.
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Idriss Boutaayamou, Salah-Eddine Chorfi, Lahcen Maniar, Omar Oukdach, The cost of approximate controllability of heat equation with general dynamical boundary conditions. Port. Math. 78 (2021), no. 1, pp. 65–99DOI 10.4171/PM/2061