Asymptotic behavior of a thermoviscoelastic plate with memory effects
Abstract
We consider a coupled linear system describing a thermoviscoelastic plate with hereditary effects. The system consists of a hyperbolic integrodifferential equation, governing the temperature, which is linearly coupled with the partial differential equation ruling the evolution of the vertical deflection, presenting a convolution term accounting for memory effects. It is also assumed that the thermal power contains a memory term characterized by a relaxation kernel. We prove that the system is exponentially stable and we obtain a closeness estimate between the system with memory effects and the corresponding memory-free limiting system, as the kernels fade in a suitable sense.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2008
- DOI:
- 10.48550/arXiv.0806.0965
- arXiv:
- arXiv:0806.0965
- Bibcode:
- 2008arXiv0806.0965G
- Keywords:
-
- Mathematics - Analysis of PDEs;
- 35B25;
- 35B35;
- 35B40;
- 45K05;
- 47D03;
- 74F05;
- 74K20
- E-Print:
- 26 pages