ȼ ɢɧɬɟɪɜɚɥɵ ɜɪɟɦɟɧɢ
T
]
a
T
1
ɢ
T
ɤ
a
T
2
&
ɤɨɬɨɪɵɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɨɛɪɚɬ
'
ɧɨɦɭ ɯɨɞɭ ɫɤɚɧɢɪɨɜɚɧɢɹ
&
ɜ ɷɥɟɤɬɪɨɧɧɨɦ ɬɪɚɤɬɟ ɩɪɨɢɡɜɨɞɢɬɫɹ ɨɛɧɭɥɟ
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ɧɢɟ ɫɢɝɧɚɥɚ
(
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ
&
ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɫɢɝɧɚɥɚ ɩɪɢ ɩɨɫɬɪɨɱɧɨ
'
ɤɚɞɪɨɜɨɦ ɫɤɚɧɢɪɨɜɚɧɢɢ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɚɦɩɥɢɬɭɞɧɨɣ ɦɨɞɭɥɹɰɢɟɣ ɷɬɨ
'
ɝɨ ɫɢɝɧɚɥɚ
&
ɱɬɨ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ ɩɪɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɦ ɦɨɞɟɥɢɪɨ
'
ɜɚɧɢɢ
(
Ⱦɥɹ ɭɞɨɛɫɬɜɚ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɩɪɨɰɟɫɫɨɜ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ
ɫɢɝɧɚɥɚ ɜ ɬɪɚɤɬɟ ɫɤɚɧɢɪɭɸɳɟɝɨ ɢɧɮɨɪɦɚɰɢɨɧɧɨɝɨ Ɉɗɉ
&
ɩɪɟɞɫɬɚɜɥɟɧ
'
ɧɨɝɨ ɧɚ ɪɢɫ
( +&
ɫɢɧɬɟɡɢɪɭɟɦ ɫɬɪɭɤɬɭɪɧɭɸ ɫɯɟɦɭ ɦɨɞɟɥɢ ɷɬɨɝɨ ɩɪɢɛɨɪɚ
ɧɚ ɫɢɫɬɟɦɨɬɟɯɧɢɱɟɫɤɨɦ ɭɪɨɜɧɟ
U0& 1W(
ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɨɫɬɚɧɨɜɤɨɣ ɡɚ
'
ɞɚɱɢ
&
ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɜ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɟ
&
ɜ ɷɬɨɣ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɟ
ɦɨɞɟɥɢ ɢɧɮɨɪɦɚɰɢɨɧɧɨɝɨ Ɉɗɉ ɧɟ ɭɱɬɟɧɨ ɞɟɣɫɬɜɢɟ ɚɞɞɢɬɢɜɧɵɯ ɩɨɦɟɯ
ɷɥɟɦɟɧɬɨɜ ɬɪɚɤɬɚ
(
ȼ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɟ
&
ɩɪɟɞɫɬɚɜɥɟɧɧɨɣ ɧɚ ɪɢɫ
( -&
ɦɨɞɟɥɶ ɢɫɬɨɱɧɢɤɚ
ɫɢɝɧɚɥɚ
+
ɨɩɢɫɵɜɚɟɬ ɫɜɨɣɫɬɜɚ ɢɡɥɭɱɟɧɢɹ ɧɚɛɥɸɞɚɟɦɨɝɨ ɨɛɴɟɤɬɚ
(
ɋɢɝ
'
ɧɚɥɨɦ ɨɬ ɨɛɴɟɤɬɚ
&
ɧɚɛɥɸɞɚɟɦɨɝɨ ɧɚ ɪɚɜɧɨɦɟɪɧɨɦ ɮɨɧɟ
&
ɜ ɷɬɨɣ ɫɢɫɬɟ
'
ɦɟ ɹɜɥɹɟɬɫɹ ɩɪɢɪɚɳɟɧɢɟ ɫɩɟɤɬɪɚɥɶɧɨɣ ɹɪɤɨɫɬɢ ɨɛɴɟɤɬɚ
(
Ȼɭɞɟɦ ɫɱɢɬɚɬɶ
&
ɱɬɨ ɷɬɨɬ ɫɢɝɧɚɥ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ
b
L
w
(
x, y, t, w
) = b
L
w
(
w
)
L
ɧ
(
x, y, t
)
,
(
,
)
ɝɞɟ
b
L
w
(
w
)
ɩɪɢɪɚɳɟɧɢɟ ɫɩɟɤɬɪɚɥɶɧɨɣ ɹɪɤɨɫɬɢ
&
L
ɧ
(
x, y, t
)
ɧɨɪɦɢ
'
ɪɨɜɚɧɧɨɟ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨ
'
ɜɪɟɦɟɧɧ
©i
ɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɹɪɤɨɫɬɢ ɧɚɛɥɸ
'
ɞɚɟɦɨɝɨ ɨɛɴɟɤɬɚ
(
Ɇɨɞɟɥɢ ɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ
,
ɢ ɮɢɥɶɬɪɚ
-
ɨɩɢɫɵɜɚɸɬ ɩɪɟɨɛɪɚɡɨɜɚ
'
ɧɢɟ ɜɯɨɞɧɨɝɨ ɨɩɬɢɱɟɫɤɨɝɨ ɫɢɝɧɚɥɚ ɜ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɫɩɟɤɬɪɚɥɶɧɨɣ ɨɫɜɟ
'
ɳɟɧɧɨɫɬɢ
b
E
w
(
x
0
, y
0
, t, w
) =
{
sin
2
}
0
A
0
~
i
(
w
)
~
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(
w
)
s
ɨɬɧ
(
w
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L
w
(
w
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×
×
L
ɧ
μ
x
0
n
,
y
0
n
, t
¶
k
H
w
o
(
x
0
, y
0
)
,
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Ɋɢɫ
( -(
ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɦɨɞɟɥɢ Ɉɗɉ
&
ɜ ɤɨɬɨɪɨɦ ɪɟɚɥɢɡɭɟɬɫɹ ɩɨɫɬɪɨɱɧɵɣ ɡɚ
'
ɤɨɧ ɫɤɚɧɢɪɨɜɚɧɢɹ
4
+
ɢɫɬɨɱɧɢɤ ɨɩɬɢɱɟɫɤɨɝɨ ɫɢɝɧɚɥɚ
5
,
ɨɩɬɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ
5
-
ɨɩɬɢɱɟɫɤɢɣ ɮɢɥɶɬɪ
5
.
ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ ɮɢɥɶɬɪ
5
/
ɉɂ
5
0& 1
ɜɪɟɦɟɧɧ
©
ɵɟ ɮɢɥɶɬɪɵ
5
2
ɦɨɞɭɥɹɬɨɪ
5
3
ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɣ ɮɢɥɶɬɪ
0 CMMH *,-0'-3--(
ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ
(
ɇ
(
ɗ
(
Ȼɚɭɦɚɧɚ
(
ɋɟɪ
(
ɉɪɢɛɨɪɨɫɬɪɨɟɧɢɟ
( ,**/(
ʋ
+
