Abstract
The purpose of the paper is to describe the boundary behavior
of the Green function of the parabolic equation
Δ
+
+ 2((∇ϕ)/ϕ)·∇
-
= 0 in
×ℝ
,
where
is a bounded
domain in ℝ
(
≥ 3),
ϕ is the positive eigenfunction
corresponding to the first eigenvalue of -Δ,
is the initial value such that
ϕ
∈
) and
belongs to a class of time dependent potentials which can be written as a nonlinear combination of derivatives of a function.