On the stabilization of a Cauchy viscoelastic problem with singular kernel and nonlinear source term

Abstract

A viscoelastic Cauchy problem subjected to a nonlinear source term is investigated. The memory term in the system involves a kernel which is not regular as is usually the case. It is proved that solutions go to zero in a polynomial manner as time goes to infinity.

Keywords:

• polynomial decay
• Cauchy problem
• singular kernel
• viscoelastic problem

AMS Subject Classifications:

• 35B05
• 35L05
• 35L15
• 35L70

Acknowledgements

The authors would like to express their sincere thanks to King Fahd University of Petroleum and Minerals for its support.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been funded by KFUPM under [Project #IN100030].