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0 < log
1 − a
1
+ a
< 2
|1 − a| > |1 + a| a < 0
|a| a < 0
1 a → −∞ a ∗ < 0 a < a ∗
a < a ∗ −∞ 0 < t ∗ a < 1 x(t)
t0 > 0 Q2
I −∞ t1 > t0 t1 ∈ I x(t0) = b < a ∗
v(t) = x(t − t0) x(t) t0 < t < t0 + 1
t > 0
t > 0 −∞
a1 < a2 < 0
x1(t) x2(t) x1(t) < x2(t) t ≥ 0
A := {a ∈ R : ta ≥ 0 ta = x 2 (a, ta)}
B :=
a ∈ R : ta ≥ 0 ta =
1
2x(a, ta) + x2 (a, ta), x(a, ta) < 0
x(a, t) a t A ⊃
[0, +∞[ B ⊃] − ∞, a ∗ ] A ∩ B = ∅ A
B a + = inf A ≤ 0 a − = sup B ≥ −1
a + /∈ A a + ∈ A ¯x(t)
¯t > 0 ¯t = ¯x 2 (¯t) ā ≤ 0 ¯x(¯t) = − √ ¯t
˙x = t − x 2 x(t0) = − √ ¯t R Q
[0, ¯t] ˙x < 0
¯t ¯x(¯t) = − √ ¯t 0 α +
α + a − /∈ B
[a − , a + ] A B
a − = a + a − < a1 < a2 < a +
d
dt (x(a1, t) − x(a2, t)) = x 2 (a1, t) − x 2 (a2, t) > 0
a1 a2
a1 − a2 > 0 t = x 2 t = 1/(2x) + x 2
a − = a + = α
R Q
α
− √ t t → +∞
Γ(z) =
+∞
0
α = − 31/3 Γ(2/3)
Γ(1/3)
−0, 729011,
t z−1 e −t dt
⎧
⎪⎨ −6∂tu(t, x) + 4∂xxu(t, x) + 3u = 0, (t, x) ∈]0, +∞[×[0, π],
∂xux(t, 0) = ∂xux(t, π) = 0
⎪⎩
u(0, x) = x(π − x).
,