Comportamento assintótico para equações de placa fracionárias

Abstract

In this work, we consider two second-order fractional semilinear plate equations in time. In the first problem, we investigate an equation governed by a biharmonic operator, with clamped boundary conditions in a smooth bounded domain, modeling flight structures. In this context, we introduce a dissipative term that depends directly on the energy of the system. In the second problem, we add a memory term, resulting in a dissipative system that depends on energy and past memory. In both cases, we study local and global well-posedness and we prove the existence of a compact global attractor for the associated evolution semigroup. Additionally, we obtain the upper semicontinuity of the family of global attractors.