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

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.