MARIA GRAZIA NASO

Exponential stability of a viscoelastic plate with thermal memoty

Pages: 37-56
Received: 5 October 1999   
Revised: 20 December 19999
Mathematics Subject Classification (2000): 35B40 - 45K05 - 73B30 - 80A20

Abstract: We study herein a two-dimensional evolution problem arising in the theory of linear thermoviscoelasticity with hereditary heat conduction. Linear semigroup theory is used to etablish the well-posedness and the exponential decay of solutions. In spite of the presence of a convolution term, the original problem is transformed into an autonomous system by suitable choice of variables. In order to achieve the exponential stability, we assume that mechanical and thermal memory kernels decay exponentially for large time and have a weak singularity at the origin.