Uniform asymptotic stability of a PDE's system arising from a flexible robotics model

In this paper we investigate the uniform asymptotic stability of a fourth-order PDE with a fading memory forcing term and boundary conditions arising from a flexible robotics model. To achieve our objective the model is rewritten in an abstract formulation by using the C_0-semigroup theory. First we provide new results on the existence, uniqueness, continuous dependence on initial data of either mild and strong solutions for semilinear integro-differential equations in Banach spaces. Then, in this abstract setting, we also find sufficient conditions for the uniform asymptotic stability of solutions and for the existence of attactors. As a consequence of these theoretical results, we can ensure existence, uniqueness and continuous dependence on initial data for the solutions of the boundary value problem related to the model, and, under suitable conditions on the nonlinear term, also the uniform asymptotic stability of solutions and the existence of attactors.