Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain

Uniform energy and L2 decay of solutions for linear wave equations with localized dissipation will be given. In order to derive the L2-decay property of the solution, a useful device whose idea comes from Ikehata–Matsuyama (Sci. Math. Japon. 55 (2002) 33) is used. In fact, we shall show that the L2-norm and the total energy of solutions, respectively, decay like and O(1/t2) as t→+∞ for a kind of the weighted initial data.