Exponential stability of the Kirchhoff plate with thermal or viscoelastic damping

Zhuangyi Liu, Songmu Zheng
1997 Quarterly of Applied Mathematics  
The exponential stability of the semigroup associated with the Kirchhoff plate with thermal or viscoelastic damping and various boundary conditions is proved. This improves the corresponding results by Lagnese by showing that the semigroup is still exponentially stable even without 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. If thermal
more » ... oblems. If thermal damping is considered, then the vertical deflection w of the plate and the temperature 6 satisfy the following partial differential equations (see [L]): w" -■yAw" + A2w + aA8 = 0, (1-2) (39' -r/AO + ad -aAw' = 0, (1-3) with a, P, rj, a > 0,7 > 0 being constants, and the prime being time derivative. Various boundary conditions could be imposed on 9 depending on what is assumed about the
doi:10.1090/qam/1466148 fatcat:6olhz6djnjh7zh6pgrzxfxz6ia