Existence and boundary stabilization of the semilinear Mindlin- Timoshenko system

We consider dynamics of the one-dimensional Mindlin-Timoshenko model for beams with a nonlinear external forces and a boundary damping mechanism. We investigate existence and uniqueness of strong and weak solution. We also study the boundary stabilization of the solution, i.e., we prove that the energy of every solution decays exponentially as $t\rightarrow\infty$

Exact controllability for the semilinear string equation in non cylindrical domains

In this paper, we investigate the exact controllability for a mixed problem for the equation u^n - [...] + f(u) = 0 in a non cylindrical domain. This model, without the resistance represented for f(u), is a linearization of Kirchhoff's equation for small vibrations of a stretched elastic string when the ends are variables, see Medeiros, Limaco, Menezes (2002). We employ a variant, due to Zuazua (1990b), of the Hilbert Uniqueness Method (HUM), idealized by Lions (1988a, b)

Hierarchical exact controllability of semilinear parabolic equations with distributed and boundary controls

We present some exact controllability results for parabolic equations in the context of hierarchic control using Stackelberg–Nash strategies. We analyze two cases: in the first one, the main control (the leader) acts in the interior of the domain and the secondary controls (the followers) act on small parts of the boundary; in the second one, we consider a leader acting on the boundary while the followers are of the distributed kind. In both cases, for each leader, an associated Nash equilibrium pair is found; then, we obtain a leader that leads the system exactly to a prescribed (but arbitrary) trajectory. We consider linear and semilinear problems. </jats:p