This work is concerned with stabilization of a wave equation by a linear boundary term combining frictional and memory damping on part of the boundary. We prove that the energy decays to zero exponentially if the kernel decays exponentially at infinity. We consider a slightly different boundary condition than the one used by M. Aassila et al. [Calc. Var. 15, 2002]. This allows us to avoid the assumption that the part of the boundary where the feedback is active is strictly star-shaped. The result...
We study in an abstract setting the indirect stabilization of systems of two wave-like
equations coupled by a localized zero order term. Only one of the two equations is
directly damped. The main novelty in this paper is that the coupling operator is not
assumed to be coercive in the underlying space. We show that the energy of smooth
solutions of these systems decays polynomially at infinity, whereas it is known that
exponential stability does not...
We study in an abstract setting the indirect stabilization of systems of two wave-like
equations coupled by a localized zero order term. Only one of the two equations is
directly damped. The main novelty in this paper is that the coupling operator is not
assumed to be coercive in the underlying space. We show that the energy of smooth
solutions of these systems decays polynomially at infinity, whereas it is known that
exponential stability does not...
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