Longtime behavior for an extensible beam equation with rotational inertia and structural nonlinear damping

The paper investigates the well-posedness, regularity and longtime behavior of solutions for an extensible beam equation with fractional rotational inertia and structural nonlinear damping: (1+(−Δ)θ)utt+Δ2u−M(‖∇u‖2)Δu+N(‖∇u‖2)(−Δ)αut+f(u)=g, with dissipative index α∈(0,1] and rotational index θ∈[0,α). We find a new critical exponent pθα≡N+2(2α−θ)(N−4)+(>p⁎=N(N−4)+) depending on both θ and α and show that when the growth exponent p of the nonlinearity f(u) is up to the range: 1≤p更多