We consider the reaction-diffusion equation
\[
T
t
=
T
x
x
+
f
(
T
)
T_t = T_{xx} + f(T)
\]
on
R
{\mathbb {R}}
with
T
0
(
x
)
≡
χ
[
−
L
,
L
]
(
x
)
T_0(x) \equiv \chi _{[-L,L]} (x)
and
f
(
0
)
=
f
(
1
)
=
0
f(0)=f(1)=0
. In 1964 Kanel
′
^{\prime }
proved that if
f
f
is an ignition non-linearity, then
T
→
0
T\to 0
as
t
→
∞
t\to \infty
when
L
>
L
0
L>L_0
, and
T
→
1
T\to 1
when
L
>
L
1
L>L_1
. We answer the open question of the relation of
L
0
L_0
and
L
1
L_1
by showing that
L
0
=
L
1
L_0=L_1
. We also determine the large time limit of
T
T
in the critical case
L
=
L
0
L=L_0
, thus providing the phase portrait for the above PDE with respect to a 1-parameter family of initial data. Analogous results for combustion and bistable non-linearities are proved as well.