Уравнения математической физики. Мицик М.Ф. - 7 стр.

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 (22) (25) .
 (22) 
x
,  (25) – 
t
,      
t
x
i
∂∂
∂
2
,  

(
)
txU ;
( )
UGR
t
U
GLRC
t
U
LC
x
U
+
∂
∂
++
∂
∂
=
∂
∂
22
.
:
( )
iGR
t
i
GLRC
t
i
LC
x
i
+
∂
∂
++
∂
∂
=
∂
∂
22
, :
wc
t
w
b
t
w
a
x
w
00
2
0
2
2 +
∂
∂
+
∂
∂
=
∂
∂
, (26)

GRc
GLRC
bLCa =
+
==
000
,
2
,
.
     
0
=
R


( )
0
=
G
, 
0
=
b

(19) 
2
2
2
2
x
w
a
t
w
∂
∂
=
∂
∂
, 
LCa =
. (27)
 ,     
, , 
   ,      
 2.
3. .
, 
. 

D
, 

Γ
.

T
.
, 
T
,

.
   . 
u
   
( )
uyxM ;;
   
( )
tyxuu ;;
=
.  
0
tt
=

( )
0
;; tyxuu
=
 
.
                 (22)   (25)                                                          .
                                                (22)                    x,                     (25) –
                                                                     ∂ 2i
t,                                                                        ,
                                                                    ∂x∂t
                    U (x; t )
                  ∂U          ∂U                 ∂U
                       = LC        + ( RC + GL )     + GRU .
                  ∂x 2        ∂t 2                ∂t
                                                                         :
                   ∂i        ∂i                ∂i
                       = LC      + ( RC + GL )    + GRi
                  ∂x 2      ∂t 2               ∂t
                              ,                                                                    :
              ∂w       ∂w       ∂w
                   = a0 2 + 2b0    + c0 w ,                                                      (26)
              ∂x 2
                       ∂t       ∂t
                        RC + GL
        a0 = LC , b0 =           , c0 = GR .
                           2
                                                                                              (R = 0)
                                                (G = 0) ,                         b=0
(19)
                            ∂w      2 ∂ w
                                       2
                                 =a        ,       a = LC .                                      (27)
                            ∂t 2      ∂x 2
                               ,
                        ,                                                ,
                                           ,
                                         2.

                        3.                                                            .

                                                                          ,
                              .
                                                             D,
          Γ.
                                                                                                   T.
                                                                                          ,       T,

                                                                              .
                                                                                  .                     u
                                                       M ( x; y; u )
u = u (x; y; t ) .                     t = t0                u = u (x; y; t 0 )
             .

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