Уравнения математической физики. Мицик М.Ф. - 8 стр.

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
( )
S
′

t
, 

( )
S

x
∆

y
∆
. 
( )
S
′


( )
22
yxo ∆+∆

x
∆

y
∆
.
 2.
    ,   , 

( )
tyxuu ;;
=
.
     
OU
,  
  .   
  ,    
1

( )
S
′
. 
M

γβα coscoscos kjin ++=
,

1
:
111
coscoscos γβα kjir ++=
.

M

[ ]
nr;
, 
, 
Sd
′

1

OU

(
)
SdT
′
−
11
coscoscoscos
β
α
β
α
.
     ,

1
, :
(
)
∫∫
ΓΓ
−=
′
−
11
1111
coscoscoscoscoscos dyxdTSdT αββαβα
, (28)

11
cos xdSd
=
′
α
11
cos ydSd
=
′
β
.
( )
yx;
M
γ
n
S
′
r
X
O
Y
U
D
Γ
1
Γ
                                                                (S ′)                                    t,
                                                                                                (S )                    ∆x
∆y .                                                                                                     (S ′)
                            (
                        o ∆ x2 + ∆ y2           )               ∆x       ∆y .

                            U


                                                                                  γ         n


                                                                                  S′
                                                            r           M
                                                                                       Γ1
                            O
                                                                                                           Y
                                                         D
                                                                         (x; y )                  Γ
       X
                                                                        2.

                                                        ,                                                        ,
                                                    u = u (x; y; t ) .
                                                                                                  OU ,
                                                            .
                                                        ,                                                                        Γ1
                  (S ′) .                                                                                                        M

                                n = i cos α + j cos β + k cos γ ,
                                                                Γ1 :
                                r = i cosα1 + j cos β1 + k cosγ 1 .
                                                    M                                                                [r; n ] ,
                                            ,                                                             dS ′                   Γ1
            OU
                                T (cos α 1 cos β − cos α cos β1 )dS ′ .
                                                                                                                                  ,
                                            Γ1 ,                :
           T ∫ (cos α 1 cos β − cos α cos β1 ) dS ′ = T ∫ cos β d x1 − cos α dy1 ,                                      (28)
             Γ1                                                              Γ1

                    cos α1dS ′ = d x1                   cos β1dS ′ = d y1 .

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