Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 73, pp. 1-14.

Title: Decay results for viscoelastic diffusion equations in absence of
       instantaneous elasticity

Author: Mohammad Kafini (KFUPM, Dhahran, Saudi Arabia)

Abstract:
 We study the diffusion equation in the absence of instantaneous elasticity
 $$
 u_t-\int_0^{t}g(t-\tau )\Delta u(\tau )\,d\tau =0,\quad (x,t)\in \Omega
 \times (0,+\infty ),
 $$
 where $\Omega \subset \mathbb{R}^n$, subjected to nonlinear
 boundary conditions. We prove that if the relaxation function
 g decays  exponentially, then the solutions is exponential stable.

Submitted December 18, 2011. Published May 10, 2012.
Math Subject Classifications: 35B05, 35L05, 35L15, 35L70.
Key Words: Diffusion equation; instantaneous elasticity; 
           exponential decay; relaxation function; viscoelastic.