On asymptotic time decay of solutions to a parabolic equation in unbounded domains

Estimates on the asymptotic behaviour of solutions to a parabolic equation are given, when the I.B.V.P. is posed in particular domains. More precisely, the domain Ω is unbounded, unbounded in any direction, and Ω is enclosed in a wedge or in a cone of two or three-dimensional Euclidean space. It is proved that the order of decay is increasing for decreasing opening of the wedge or of the cone.