ABSTRACT
Theorem 9.95 Consider the Cauchy problem (1) for u0 ∈ L2ρ∗(IRN ) and u0 = 0. Then, there exists a finite integer l ≥ 0 and a function ϕl(y), such that, as t → +∞,
u(x, t) = t− N+l 2m
[ ϕl (
) +O
( t−
)] (90)
uniformly on compact sets in y = x t1/2m
, where ϕl(y) is a nontrivial superposition of extended eigenfunctions {ψβ, |β| = l} of B from the corresponding finite-dimensional eigenspace.
