Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 25, No 3, (1999), 191p-206p
It is proved in , that in odd dimensional spaces any uniform decay
of the local energy implies that it must decay exponentially. We
extend this to even dimensional spaces and to more general perturbations
(including the transmission problem) showing that any uniform decay of the
local energy implies that it must decay like O(t^(−2n) ), t ≫ 1 being the time
and n being the space dimension.