Internal stabilization of the plate equation in a square : the continuous and the semi-discretized problems.Report as inadecuate




Internal stabilization of the plate equation in a square : the continuous and the semi-discretized problems. - Download this document for free, or read online. Document in PDF available to download.

1 IECN - Institut Élie Cartan de Nancy 2 CORIDA - Robust control of infinite dimensional systems and applications IECN - Institut Élie Cartan de Nancy, LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est

Abstract : This paper is devoted to the study of the internal stabilization of the Bernoulli-Euler plate equation in a square. The continuous and the space semi-discretizated problems are successively considered and analyzed using a frequency domain approach. For the infinite dimensional problem, we provide a new proof of the exponential stability result, based on a two dimensional Ingham-s type result. In the second and main part of the paper, we propose a finite difference space semi-discretization scheme and we prove that this scheme yields a uniform exponential decay rate with respect to the mesh size.

Keywords : Plate equation Stabilization Uniform exponential stability Finite-difference





Author: Karim Ramdani - Takeo Takahashi - Marius Tucsnak -

Source: https://hal.archives-ouvertes.fr/



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