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
Grasselli, M., Munoz Rivera, J. E., Squassina, M., Asymptotic behavior of a thermoviscoelastic plate with memory effects, <<ASYMPTOTIC ANALYSIS>>, 2009; 63 (N/A): 55-84. [doi:10.3233/ASY-2008-0928] [http://hdl.handle.net/10807/90745]
Asymptotic behavior of a thermoviscoelastic plate with memory effects
Squassina, MarcoUltimo
2009
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 senseI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.