×

Convergence of the boundary control for the wave equation in domains with holes of critical size. (English) Zbl 1007.35007

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.

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
PDFBibTeX XMLCite
Full Text: EuDML EMIS