A numerical method of local energy decay for the boundary controllability of time-reversible distributed parameter systems

摘要

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.