Electron. J. Diff. Equ., Vol. 2012 (2012), No. 73, pp. 1-14.

Decay results for viscoelastic diffusion equations in absence of instantaneous elasticity

Mohammad Kafini

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.

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Mohammad Kafini
Department of Mathematics and Statistics
KFUPM, Dhahran 31261
Saudi Arabia
email: mkafini@kfupm.edu.sa

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