Electron. J. Diff. Equ., Vol. 2011 (2011), No. 93, pp. 1-9.

Uniform decay of solutions to Cauchy viscoelastic problems with density

Mohammad Kafini

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.

Submitted May 25, 2011. Published July 18, 2011.
Math Subject Classifications: 35B05, 35L05, 35L15, 35L70
Key Words: Cauchy problem; relaxation function; viscoelastic; weighted spaces.

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

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