On the decay of solutions to the 2D Neumann exterior problem for the wave equation. (Q1413206)

The mixed problem for the wave equation with Neumann boundary condition is considered. In the paper [Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation. II, Rend. Semin. Mat. Univ. Padova 108, 67--77 (2002; Zbl 1072.35110)], the first author of this article was already concerned with the asymptotic behaviour of the solution for large times. The aim of the present paper is to get a decay estimate which does not depend on weighted norms of the data. This is achieved by combining local energy decay estimates with decay estimates for the free space solution.