Уравнения математической физики. Уравнение теплопроводности. Хуснутдинов Н.Р. - 11 стр.

UptoLike

Составители: 

G = g
4x
l
, f(x) = T |
x
l
1
2
| sin
2πx
l
.
G = g
x
3l
cos
3πvt
l
, F (x) = 0, f (x) =
l
3
(1 cos
πx
l
), 0 x l/2
4
3l
(x l)
2
, l/2 x l
ψ = g
v
2
t
2
l
2
e
2πvt/l
φ = 0
, f(x) = 0 , F (x) =
x(xl)
h
cos
πx
4l
.
f(x) = T
0 , 0 x l/4
(xl/4)(3l/4x)
l
2
, l/4 x 3l/4
0 , 3l/4 x l
.
f(x) = T
(
3x
2
l
2
, 0 x l/5
3(xl)
2
16l
2
, l/5 x l
.
G = g
2x
2
l
2
, f(x) = T
x(3l/4x)
l
2
, 0 x 3l/4
0 , 3l/4 x l
.
G = g
1 e
2x
l
sin
πvt
l
, f(x) = 0, F (x) =
3
l
x
2
, 0 x l/7
1
12l
(x l)
2
,l/7 x l
φ = g
e
3πvt
l
1
ψ = 0
, F (x) = 0, f (x) =
0, 0 x l/4
(xl/4)(l/2x)
h
,l/4 x l/2
0, l/2 x l
f(x) = T
|x
l
2
|
l
sin
2πx
l
.
f(x) = T
1
3
(1 cos
πx
l
) , 0 x l/2
4
3l
2
(x l)
2
, l/2 x l
.
G = g
e
x/l
+ 1
, f(x) = T
(xl)
2
l
2
sin
πx
4l
.
G = g
x
2
l
2
sin
πvt
l
, F (x) = 0, f(x) =
l
5
(1 cos
πx
l
), 0 x l/3
9
40l
(x l)
2
l/3 x l
ψ = g
e
πvt/l
e
πvt/l
φ = 0
, f(x) = 0 , F (x) =
x(xl)
h
cos
2πx
l
.
f(x) = T
x(3l/4x)
l
2
, 0 x 3l/4
0 , 3l/4 x l
.
f(x) = T
3
l
2
x
2
, 0 x l/6
3
25l
2
(x 2)
2
l/6 x l
.
G = ge
2x/l
, f(x) = T
0 , 0 x 3l/4
(xl)(3l/4x)
l
2
, 3l/4 x l
.
G = g
3x
l
e
x
l
cos
3πvt
l
, f(x) = 0, F (x) =
3
l
x
2
, 0 x l/8
3
49l
(x l)
2
,l/8 x l
φ = g
e
πvt
2l
e
πvt
2l
ψ = 0
, F (x) = 0, f(x) =
0, 0 x l/8
(x
l
8
)(
l
2
x)
h
,l/8 x l/2
0, l/2 x l
f(x) = T
(xl)
2
l
2
sin
πx
4l
.
f(x) =
4(1 cos
πx
l
) , 0 x l/4
64
9l
2
(1
2
2
)(x l)
2
l/4 x l
.
G = g
3x
2
l
2
x
l
, f(x) = T
x(xl)
l
2
cos
πx
4l
.
G = g
x
2
l
2
sin
2πvt
l
, F (x) = 0, f(x) =
4l(1 cos
πx
l
), 0 x l/5
25
4l
(1 cos
π
5
)(x l)
2
,l/5 x l
ψ = g
vt
l
e
πvt/2l
φ = 0
, f(x) = 0 , F (x) =
x(xl)
h
cos
πx
l
.
f(x) = T
0 , 0 x 3l/4
(xl)(3l/4x)
l
2
, 3l/4 x l
.
f(x) = T
3
l
2
x
2
, 0 x l/7
1
12l
2
(x l)
2
, l/7 x l
.
G = g
x
3l
, f(x) = T
0 , 0 x l/4
(xl/4)(l/2x)
l
2
, l/4 x l/2
0 , l/2 x l
.
G = g
x
2
l
2
+ e
x
l
cos
2πvt
l
, f(x) = 0, F (x) =
3
l
x
2
, 0 x l/9
3
64l
(x l)
2
,l/9 x l
φ = g
v
2
t
2
l
2
e
πvt
3l
ψ = 0
, F (x) = 0, f (x) =
0, 0 x l/8
(x
l
8
)(
l
4
x)
h
, l/8 x l/4
0, l/4 x l
                                                                                                                    3 2
                                                                                                                
3.   G = g 4x               x   1      2πx
            l , f (x) = T | l − 2 | sin l .                                                    2.   f (x) = T       l2 x ,        0 ≤ x ≤ l/6
                                                                                                                                                 .
                                                                                                                      3
                                                         − 3l (1 − cos πx                                                − 2)2 l/6 ≤ x ≤ l
                                                                                                                    25l2 (x
                                                    
           x
     G = g 3l cos 3πvt                                                    l ),   0 ≤ x ≤ l/2
4.
                    l , F (x) = 0, f (x) =
                                                                                                                               
                                                            4
                                                         − 3l  (x − l)2 ,        l/2 ≤ x ≤ l             −2x/l                    0,                0 ≤ x ≤ 3l/4
                                                                                               3. G = ge       , f (x) = T        (x−l)(3l/4−x)                         .
             2 2
     ψ = g vl2t e2πvt/l                                    x(x−l)                                                                       l2      , 3l/4 ≤ x ≤ l
5.                      , f (x) = 0 , F (x) =                       cos πx
                                                                        4l .
                                                                                                                                                     3 2
                                                                                                                                                        lx ,           0 ≤ x ≤ l/8
     φ=0                                                     h
                                                                                                         3x      − xl
                                                                                                                        cos 3πvt
                                                                                                                      
                                                                                               4. G = g
                                                                                                          l −e                l , f (x) = 0, F (x) =     3           2
                                                                                                                                                            (x − l) ,l/8 ≤ x ≤ l
                                                                                                                                                    49l
                                                 7                                                      πvt          πvt
                                                                                                                                                     0,            0 ≤ x ≤ l/8
                                                                                                  φ = g e− 2l − e 2l
                                                                                                                                                    l l
                                                                                                                                                    (x− 8 )( 2 −x)
                                                                                              5.                            , F (x) = 0, f (x) =                  ,l/8 ≤ x ≤ l/2
                    0,                          0 ≤ x ≤ l/4                                      ψ=0                                                      h
                                                                                                                                                      0,            l/2 ≤ x ≤ l
                                                                                                                                                   
                        (x−l/4)(3l/4−x)
1.   f (x) = T                 l2           ,    l/4 ≤ x ≤ 3l/4 .
                0,                               3l/4 ≤ x ≤ l
              
              (        2
                                                                                                                                          10
                − 3x l2 , 2          0 ≤ x ≤ l/5
2. f (x) = T                                        .
                − 3(x−l)       ,     l/5 ≤ x ≤ l                                                  f (x) = T (x−l)
                                                                                                                     2
                                                                                                                      sin πx
                                                                                                                           4l .
                      16l2                                                                    1.
                                  x(3l/4−x)
                                             , 0 ≤ x ≤ 3l/4                                                 l2
          2x2
3. G = g 2 , f (x) = T                 l2                          .                                          4(1 − cos√ πx   l ) ,          0 ≤ x ≤ l/4
           l                      0,              3l/4 ≤ x ≤ l                                 2. f (x) =      64           2                               .
                                                                                                                                        2
                                                                                                                  (1 −        )(x − l) l/4 ≤ x ≤ l
                                                           3 2                                           2 9l2  2
                                                            lx ,        0 ≤ x ≤ l/7
                     
                − 2x
4. G = g 1 − e     l     sin πvtl  , f (x) = 0, F (x) =      1         2                       3. G = g
                                                                                                           3x       x
                                                                                                            l2 − l , f (x) = T
                                                                                                                                        x(x−l)
                                                                                                                                               cos πx .
                                                            12l (x − l)  ,l/7 ≤ x ≤ l                                                     l2
                                                                                                                                                4l
                                                                                                                                                4l(1 − cos πx l ),         0 ≤ x ≤ l/5
                                                   
                                                    0,               0 ≤ x ≤ l/4                       x2      2πvt
          3πvt       
   φ=g e l −1                                                                                  4. G = g 2 sin         , F (x)   =  0, f (x)  =   25           π         2
                                                      (x−l/4)(l/2−x)                                    l         l                                 (1 − cos    )(x − l)  ,l/5 ≤x≤l
5.                        , F (x) = 0, f (x) =              h        ,l/4  ≤ x ≤ l/2                                                             4l           5
   ψ=0                                                                                                   vt πvt/2l
                                                   
                                                      0,              l/2 ≤ x ≤ l                 ψ=g le
                                                                                               5.                      , f (x) = 0 , F (x) = x(x−l)   h   cos πxl .
                                                                                                  φ=0
                                                 8
                                                                                                                                          11
                   |x− 2l |         2πx
1.   f (x) = T     l         sin    l .
                                                                                                                
                                                                                                                    0,                0 ≤ x ≤ 3l/4
                   − 31 (1 − cos πx l ) ,    0 ≤ x ≤ l/2                                       1.   f (x) = T       (x−l)(3l/4−x)                     .
2.   f (x) = T                                               .                                                                       ,3l/4 ≤ x ≤ l
                   − 3l42 (x − l)2 ,         l/2 ≤ x ≤ l                                                           3 2
                                                                                                                           l2
                                             2                                                                      l2 x  ,         0 ≤ x ≤ l/7
                                                                                               2. f (x) = T                                        .
     G = g ex/l + 1 , f (x) = T (x−l)          sin πx
                       
3.                                                    .                                                               1
                                                                                                                               l)2 ,
                                          l2    4ll             πx                                                 12l2 (x −       l/7 ≤ x ≤ l
                                                  −  5 (1 − cos l ), 0 ≤ x ≤ l/3
                                                                                                                             
4.
             2
     G = g xl2 sin πvt , F (x) =   0, f (x)  =        9
                                                                                                                           0,                   0 ≤ x ≤ l/4
                    l                             − 40l  (x − l)2     l/3 ≤ x ≤ l                        x
                                                                                               3. G = g , f (x) = T
                                                                                                                             (x−l/4)(l/2−x)
                                                                                                                                             , l/4 ≤ x ≤ l/2 .
               −πvt/l      πvt/l
                                                                                                        3l                         l2
     ψ=g e            −e                                       x(x−l)
                                                                                                                          
                                                                                                                             0,                  l/2 ≤ x ≤ l
5.                                   , f (x) = 0 , F (x) = h cos 2πx     l .
     φ=0                                                                                                                                              3 2
                                                                                                                                                           lx ,         0 ≤ x ≤ l/9
                                                                                                         2        x
                                                                                                                     
                                                                                                            x              2πvt
                                                                                               4. G = g
                                                                                                            l2 + e     cos l , f (x) = 0, F (x) =
                                                                                                                   l
                                                                                                                                                            3        2
                                                                                                                                                          64l (x − l)  ,l/9 ≤x≤l
                                                 9
                                                                                                                                             0, l l             0 ≤ x ≤ l/8
                                                                                                                                            
                                                                                                          2 2    πvt
                       x(3l/4−x)                                                                 φ = g vl2t e− 3l                             (x− 8 )( 4 −x)
                                       ,   0 ≤ x ≤ 3l/4                                        5.                     , F (x) = 0, f (x) =                    , l/8 ≤ x ≤ l/4
1.   f (x) = T              l2                          .                                         ψ=0                                                h
                       0,                  3l/4 ≤ x ≤ l                                                                                        0,                l/4 ≤ x ≤ l
                                                                                                                                            


                                                 21                                                                                     22