International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 10, Pages 1497-1506
doi:10.1155/IJMMS.2005.1497
Asymptotic behavior for a nonlinear viscoelastic problem with a
velocity-dependent material density
Department of Mathematical Sciences, College of Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Received 22 September 2004; Revised 10 May 2005
Copyright © 2005 Nasser-Eddine Tatar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider a nonlinear viscoelastic problem and prove that the solutions are uniformly bounded and decay exponentially to zero as time goes to infinity. This is established under weaker conditions on the relaxation function than the usually used ones. In particular, we remove the assumptions on the derivative of the kernel. In fact, our kernels are not necessarily differentiable.