Stabilization and control for the subcritical semilinear wave equation

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Uniformly exponentially stable approximations for a class of damped systems (2009, background): “For instance, in [10] (see also [29,30]), the exponential decay property of solutions of semilinear wave equations in R3 with a damping term which is effective on the exterior of a ball are analyzed.”
Stabilization for the semilinear wave equation with geometric control condition (2012, methodology): “The proof is exactly the same as that of Theorem 3 of [Dehman et al. 2003] or Theorem 3.”
The Wave Equation: Control and Numerics (2012, background): “More recently, using dispersive estimates (see [25, 24]), the class of nonlinearities for which this kind of results holds has been extended to cover the range of nonlinearities that can be handled for the well-posedness of the Cauchy problem in the energy space by means of Strichartz inequalities.”
Unique continuation and decay for the Korteweg-de Vries equation with localized damping (2005, methodology): “More recently the problem of decay for locally dissipated semilinear wave equation was analyzed by Dehman, Lebeau and Zuazua in [3].”