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Nonlinear internal feedbacks of the Euler-Bernoulli plate equations with Variable Coefficients

We consider the energy decay for solutions of the Euler-Bernoulli plate equation with variable coefficients where a nonlinear internal feedback acts in a part of the domain. Our interest is in studying the structure of control regions which guarantees decays of solutions, where the plate is fixed on the boundary. Our results show that the structure of a control region depends not only on the type of boundary conditions but also on the curvature of a Riemannian metric, based on the coefficients of the system. Some geometrical conditions are presented to obtain a control region.