Decay estimate in a viscoelastic plate equation with past history, nonlinear damping, and logarithmic nonlinearity

Abstract

Abstract In this article, we consider a viscoelastic plate equation with past history, nonlinear damping, and logarithmic nonlinearity. We prove explicit and general decay rate results of the solution to the viscoelastic plate equation with past history. Convex properties, logarithmic inequalities, and generalized Young’s inequality are mainly used to prove the decay estimate.

Keywords

• Viscoelasticity
• Local existence
• Convexity
• Decay estimate
• Logarithmic nonlinearity