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We consider the exact controllability of the Euler-Bernoulli plate equation with variable coefficients and mixed boundary conditions. By using the Riemannian geometrical approach and the multiplier technique, we establish the corresponding observability inequality and obtain the exact controllability results.
We consider the existence of global solutions of the nonlinear elastodynamic system with a boundary dissipation structure when initial data are small. The medium material is assumed to be isotropic and hyperelastic. We show the existence of global smooth solutions. In particular, we obtain the exponential decay of the energy, which implies the exponential stabilization of the system by boundary feedback.
We study the existence of global smooth solutions for the quasilinear wave equations with internal locally damping when initial data are near a given equilibrium. Our interest is to study the effect of the damping region which guarantees the existence of global solutions. Our results show that the structure of the damping region depends on geometric properties of a Riemannian metric, given by the...
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