Uniform boundary controllability of a fully discrete linear Kdv equation via discrete Carleman estimates

This article examines a well-known analogue concept of null controllability in a discrete setting, referred to as ϕ-null controllability, specifically for a fully discrete approximation of the linear Korteweg–de Vries (KdV) equation using a single boundary control. To conduct this study, we first derive a suitable Carleman estimate for a fully discrete approximation of the differential operator ∂ t + ∂ t 3. Wethen use this discrete Carleman estimate to deduce a uniform discrete observability estimate satisfied by the solution of fully-discrete adjoint system associated to the discrete control system. Finally, we illustrate how this uniform discrete observability inequality satisfied by the solution of discrete adjoint system establishes the ϕ-null controllability of the underlying discrete control system.