Decay rate of a weakly dissipative viscoelastic plate equation with infinite memory

Abstract

Abstract In this paper, a weakly dissipative viscoelastic plate equation with an infinite memory is considered. We show a general energy decay rate for a wide class of relaxation functions. To support our theoretical findings, some numerical illustrations are presented at the end. The numerical solution is computed using the popular finite element method in space, combined with time-stepping finite differences.

Keywords

• 35B40
• 35L90
• 45K05
• 65M06
• 65M60