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

Karim Ramdani (1, 2) , Takeo Takahashi (1, 2) , Marius Tucsnak (1, 2)

1 IECN - Institut Élie Cartan de Nancy
2 CORIDA - Robust control of infinite dimensional systems and applications

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).

Mots clés: Plate equation; Stabilization; Uniform exponential stability; Finite-difference

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Karim Ramdani, Takeo Takahashi, Marius Tucsnak. Internal stabilization of the plate equation in a square : the continuous and the semi-discretized problems.. Journal de Mathématiques Pures et Appliquées, 2006, 85 (1), pp.17-37. ⟨10.1016/j.matpur.2005.10.006⟩. ⟨hal-00091373⟩