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The exponential decay of the local energy for wave equations in exterior domains of the odd dimensional space has been proved in  ~  etc. under the Dirichlet boundary condition and in ,  under the Neumann condition and the other conditions. In this paper, we shall consider this problem for the following equation:doi:10.1017/s0027763000017864 fatcat:e2s5glf6r5efrdr5klxunnx4sy