Lebeau–Robbiano Inequality for Heat Equation with Dynamic Boundary Conditions and Optimal Null Controllability - Maniar, Lahcen; Oukdach, Omar; Zouhair, Walid (Differential equations and dynamical systems, 2025)
The paper deals with time and norm optimal control problems for the heat equation with dynamic boundary conditions in the context of the null controllability. More precisely, we answer an open question left in our previous paper (Boutaayamou et al., in Math Methods Appl Sci 45:1359–1376, 2021). To do so, we first prove a new Lebeau–Robbiano spectral inequality using a logarithmic convexity inequality, then an observability inequality on any set of positive measure. This plays a relevant role in proving the existence and uniqueness of optimal null controls. Finally, the connection between time and norm optimal null controls is presented.