We study the energy decay rates of the wave equation in a domain where boundary damping is present. We generalize the geometrical conditions obtained earlier in (J. Math. Purer Appl., 58 (1979), pp. 249–273) by using some more general multipliers of Strauss (Comm. Pure Appl. Math., 28 (1975), pp. 265–278). The interaction between distributed damping and boundary damping is discussed. A regulator problem is also formally discussed by the synthesis method.
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Goong Chen (1981) studied this question.
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