Nandakumaran, A. K. Convergence of the boundary control for the wave equation in domains with holes of critical size. (English) Zbl 1007.35007 Electron. J. Differ. Equ. 2002, Paper No. 35, 10 p. (2002). The author considers the homogenization \((\varepsilon\to 0)\) of the exact controllability problem for the wave equation in an \(\varepsilon\)-periodically perforated domain with small holes of critical size, assuming that the perforations are located uniformly (with respect to \(\varepsilon)\) away from the boundary. He proves weak convergence of the outer boundary control of the homogenized system. The convergence of the internal boundary controls is not studied. Reviewer: Dan Polisevski (Bucureşti) MSC: 35B37 PDE in connection with control problems (MSC2000) 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 93B05 Controllability 35L05 Wave equation 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory Keywords:perforated domain; exact controllability; Hilbert uniqueness method; outer boundary control; internal boundary controls PDFBibTeX XMLCite \textit{A. K. Nandakumaran}, Electron. J. Differ. Equ. 2002, Paper No. 35, 10 p. (2002; Zbl 1007.35007) Full Text: EuDML EMIS