Abstract
For a higher dimensional Petrovsky equation in a bounded domain with linear damping and rigid homogeneous boundary conditions, the uniformly exponential energy decay is proved by a priori estimates and analysis of Lyapunov-like functional. The global exact controllability is shown by the energy decay result and time-reverse technique. For the Petrovsky equation with cubic nonlinear damping, it is proved that for any given energy bound of initial data there exists a choice of damping coefficients such that the nonlinear semigroup of solutions converges to zero strongly and uniformly.
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