arXiv:2611.14751v1 Announce Type: new Abstract: This work investigates the stabilization of a wave equation with a localized damping and dynamic boundary conditions. This model traces back to the classical treatment of torsion and impact problems. Consider a second-order hyperbolic equation posed with a dynamic boundary condition on a smooth compact Riemannian manifold $(\M,g)$ with boundary, in which the damping acts either in the interior or on $\d \M$. Under the assumption that the damping is positive on an open subset of its domain of action, a resolvent estimate is established. A logarithmic decay rate is then deduced for the energy of strong solutions. We provide examples that establish the sharpness of the resolvent estimate.
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