Abstract: We consider the problems for linear and semilinear wave equations in
exterior domain. The authors first derive total energy decay for linear
damped wave equation. This result can be applied to the proof of the global existence for semilinear wave equation with nonlinear term |u|^psatisfies 2+. For this purpose the authors deal with a radially symmetric solution in the N-D (3≤ N≤ 7) exterior domain

Key words: Semilinear, Wave equation, Dissipation, Exterior domain