Uniform decay of solutions to Cauchy viscoelastic problems with density

Abstract

In this article we consider the decay of solutions to a linear Cauchy viscoelastic problem with density. This study includes the exponential and polynomial rates as particular cases. To compensate for the lack of Poincare's inequality in the whole space, we consider the solutions in spaces weighted by the density.

Keywords

• Cauchy problem
• relaxation function
• viscoelastic
• weighted spaces