Issue 52
O. Kryvyi et alii, Frattura ed Integrità Strutturale, 52 (2020) 33-50; DOI: 10.3221/IGF-ESIS.52.04
2
j
1
3 3 j
3 0 1 2 3 [ , , , ] ( 1)
j k
j
,
1, 2
j
k
0
2
2
7 0 1 2 3 [ , , , ]
8 0 1 2 3 [ , , , ]
j
j
θ (
j
,
θ ( ) z
z
)
,
02 3 0
02 3 0
2
2
2
1 ) , j
0,1, 2 j ,
j
j
θ (
θ ( ) z
z
1
1
2
j j
b b
a a
(
)
2
2
13 33 c
j
( c
j
j
),
,
0,1, 2
j
j
3 2 j
1
1
2
1
1
2 2 0 33 44 0 ( c c
11 33 13 13 ( ( c c c c
44 2 ))) c
11 44
c c
22
,
0
,
02
12
2 1 0
b
a
(
)
1
3 13 44 ( ) c c
3 44 ,
1 44 ,
3 11 1 13 44 ( ) c c , c
c
c
b
c
b
a
a
,
1
1 33
2
1
2
0 ( )
3 ( )
2
1
2
1
1 3 ( ) , k k
66 44 ( ) , c c
(
Constants j
1, 2 j ) are solutions of equations
13 13
44 2 ) c
11 44 c c
4
2
( ) [ ( c c
]( )
c c
c c
0.
j
j
33 44
11 33
, j j
0,1, 2, 3
satisfy the differential equations:
The functions
1 2 3 , , z 0, j
P
0
(A.4)
j
) ,
2 2 , 2 ( ) ( )
θ ( )( ) z
)( )
2 3
2 2
2
2
θ ( ) P z P
θ (
θ (
.
z P
P
z
j
j
j
j
j
j
j
j
1
3 ( ), As a result, we obtain
Following [15] we let's pass in the Eqns. (A.4) to the space of generalized functions
,( j j
0,1, 2, 3)
boundary value problems for the functions
1
1 2 3 [ , , ] j
k
k
1 3
3
(
P
f
f
( ) z
,
,
)
(A.5)
j
j
j
j
j
2
k
0
0 1 2 3 [ , , , j
0 1 2 3 [ , , , j
3 ( ),
j
( , ), x y
j
]
]
1,8,
j
(A.6)
k with generalized ones k . Applying the
j by replacing in operators
j ordinary derivatives
We obtain operators
3 ( ), by parameter
three-dimensional Fourier transform to Eqns. (A.5) we obtain the Riemann problem in the space
3 to determine the transformants of the functions , j j
0,1, 2, 3
.
p
(A.7)
p
, Q j
0, 3
j
j
j
46
Made with FlippingBook Publishing Software