Zy. Liu et Sm. Zheng, EXPONENTIAL STABILITY OF THE KIRCHHOFF PLATE WITH THERMAL OR VISCOELASTIC DAMPING, Quarterly of applied mathematics, 55(3), 1997, pp. 551-564
The exponential stability of the semigroup associated with the Kirchho
ff plate with thermal or viscoelastic damping and various boundary con
ditions is proved. This improves the corresponding results by Lagnese
by showing that the semigroup is still exponentially stable even witho
ut feedback control on the boundary. The proof is essentially based on
PDE techniques and the method is remarkable in the sense that it also
throws light on applications to other higher-dimensional problems.