Stability of strong exponential attractors for the Kirchhoff wave model with structural nonlinear damping

Abstract

This paper investigates the stability of strong exponential attractors with respect to dissipative index θ∈[1/2,1) for the Kirchhoff wave model with structural nonlinear damping: utt−ϕ(‖∇u‖2)Δu+σ(‖∇u‖2)(−Δ)θut+f(u)=g(x). It proves that for each θ0∈[1/2,1), there exists a family of strong bi-space exponential attractors, which are also the standard exponential attractors of optimal regularity and are Hölder continuous at the point θ0 in the topology of the strong solution space provided that the nonlinearity f(u) is of the optimal subcritical growth. The method used here allows to overcome the difficulties in literatures before to get the Lipschitz continuity and quasi-stability of the evolution semigroup Sθ(t) to obtain the desired result.