Stabilization of the critical semilinear wave equation on non-compact Riemannian manifold (Q6058854)

In this paper, a damped semilinear wave equation, with critical nonlinearity, on a non-compact Riemannian manifold is analyzed. In particular, the space variable belongs to an exterior domain \(\Omega=\mathbb{R}^3\setminus \mathcal{O}\), where \(\mathcal{O}\subset \mathbb{R}^3\) is a compact obstacle with a smooth boundary which is geodesically concave in the Riemannian metric. The locally distributed damping is effective outside a bounded set. Under suitable assumptions on the Riemannian metric, the authors use geometric multiplier techniques to obtain unique continuation results. Then, compactness-uniqueness arguments allow to obtain observability inequalities. Finally, a polynomial decay estimate for the energy is obtained.