Attractors and upper semicontinuity for an extensible beam with nonlocal structural damping

Abstract We analyze the asymptotic behavior of a class of extensible beam models governed by a nonlocal structural damping mechanism of the form , where . The coefficient is a degenerate ‐function depending on the linear energy of the system and determines the intensity of the damping. Our main result establishes that, for each , the ‐semigroup generated by the weak solutions of the problem admits a compact global attractor , where denotes the unstable manifold emanating from the set of stationary points. Moreover, we show the upper semicontinuity of the family of global attractors with respect to the fractional exponent .