Chjimin Guo matematika va axborot fanlari maktabi, ÿ Muallif: Zhiming Guo

t
Endi t ÿ 0 uchun s(t) = s0 + smint bo‘lsin ,
ÿ 0,
t
ÿty ÿ Dÿxxy = ky 1 ÿ
(g ÿ 1)(M1 + a) ÿ gV (s0)
va
a
s(t)
=
u¯x(t, 0) < 0, y¯x(t, 0) < 0 barcha t ÿ 0 uchun (Lemma 3.7 bo'yicha).
ÿÿÿÿÿÿÿÿ
ÿÿÿÿÿÿÿÿ
(t) = ÿµr ÿxy(t, h(t)),
Taqqoslash tamoyiliga ko‘ra, biz h(t) ÿ h(t) ga ega bo‘lamiz. [5] dagi 4.2 teoremadan biz bor
t
va
t > 0, 0 < x < h(t),
+ V (s0)
g - 1
' s
yx (t, 0) = 0,
lU(s0)
u¯t ÿ u¯xx ÿ u¯(1 ÿ u¯) = l (l ÿ 1) U ÿ l ÿ 1
h(t)
lim sup ÿ lim tÿ+ÿ
muammo
M1 + a
u¯ = lU(x ÿ smint) ÿ lU(s0) va ¯y = gV (x ÿ smint) ÿ gV (s0) t ÿ 0 va 0 ÿ x ÿ s(t) uchun.
h
y¯
t > 0,
gk
(t) = smin > ÿµ(¯ux(t, s(t)) + rÿ¯x(t, s(t)))).
(44)
h(t)
ÿ sÿ. (y, h) erkin chegaraning yechimi bo'lsin. Endi lim inf t ni
isbotlaymiz
l ÿ 1 ÿ lU(s0)
va
.
y
(41) va (43) dan ko'rinib turibdiki
Machine Translated by Google

---

0
'
1
'
'
'
T
0
0
'
'
'
h0 8(1+h˜)
15
Erkin chegaraga ega Lesli-Gower modeli
'
h0
h0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ
=
shunday qilib, xaritalash (t, x) ÿ (t, y) diffeomorfizmdir.
Uy(t, 0) = Vy(t, 0) = U(t, h0) = V (t, h0) = 0,
0 ÿ x ÿ h(t) ÿ 0 ÿ y ÿ h0 va x = h(t) ÿ y = h0.