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This paper is concerned with dynamics of elasticity systems featuring a nonlinear foundation of critical growth and delay effects. The existence of global attractors for such systems has been studied recently. Our main contribution establishes the upper-semicontinuity of attractors with respect to a small parameter multiplying the delay term. Our results are new even for the analogous scalar wave equation.

This paper is concerned with a viscoelastic Kirchhoff plate featuring variable material density. It is modeled by the equation ϱutt−Δutt+normalΔ2u−M∫normalΩ|∇ufalse|2dxΔu−∫0tg(t−s)normalΔ2u(s)ds=0, defined in a bounded domain of RN, where ϱ = |ut|ρ accounts for a velocity‐dependent material density. It is known that its analogue second‐order wave equation can be exponentially stabilized with the sole dissipation given by the memory term. However, for the plate equation, exponential stability was only shown with an additional strong damping −Δut. Our objective is to show the exponential stability of the present system by exploring only the memory term.

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