Abstract: We study the problem of stabilization of dissipative nonlinear PDE's employing finite-parameters feedback control algorithms. Specifically, we consider the problem of stabilization of steady state solutions of initial boundary value problems for nonlinear weakly and strongly damped wave equations, nonlinear wave equation with nonlinear damping term, Cahn-Hilliard equation and phase-field equations, introducing a feedback control terms that employ parameters,
such as, finitely many Fourier modes, finitely many volume elements and
finitely many nodal observables and controllers.