A Numerical Method of Local Energy Decay for the Boundary Controllability of Time‐Reversible Distributed Parameter Systems

Abstract

This paper deals with the numerical computation of the boundary controls of linear, time‐reversible, second‐order evolution systems. Based on a method introduced by Russell (Stud. Appl. Math. LII(3) (1973)) for the wave equation, a numerical algorithm is proposed for solving this type of problems. The convergence of the method is based on the local energy decay of the solution of a suitable Cauchy problem associated with the original control system. The method is illustrated with several numerical simulations for the Klein–Gordon and the Euler–Bernoulli equations in 1D, the wave equation on a rectangle, and the plate equation on a disk.