Контрольные работы по уравнениям математической физики. Ковтанюк А.Е. - 15 стр.

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3. u
t
= a
2
u
xx
+ 2x + 1, 0 < x < 1, t > 0,
u(0, t) = 1, u
x
(1, t) = 2,
u(x, 0) = 2x + 1.
4. u
t
= a
2
u
xx
+ x + 1, 0 < x < 1, t > 0,
u(0, t) = 0, u(1, t) = 1,
u(x, 0) = x.
5. u
t
= a
2
u
xx
+ 2x + 1, 0 < x < 1, t > 0,
u
x
(0, t) = 2, u(1, t) = 1,
u(x, 0) = 2x − 1.
6. u
t
= a
2
u
xx
+ x + 2, 0 < x < 1, t > 0,
u(0, t) = 0, u
x
(1, t) = 1,
u(x, 0) = x.
7. u
t
= a
2
u
xx
+ t, 0 < x < 1, t > 0,
u(0, t) = 2t, u(1, t) = 1,
u(x, 0) = x − 3sin2πx.
8. u
t
= a
2
u
xx
+ 2xt, 0 < x < 1, t > 0,
u
x
(0, t) = −1, u(1, t) = t,
u(x, 0) = 1 − x − cos
7π
2
x.
9. u
t
= a
2
u
xx
+ 2t
3
, 0 < x < 1, t > 0,
u(0, t) = 1, u
x
(1, t) = 2t,
u(x, 0) = 1 + sin
5π
2
x.
10. u
t
= u
xx
+ t
2
− 1, 0 < x < 1, t > 0,
u
x
(0, t) = 5, u
x
(1, t) = −1,
u(x, 0) = 2 + 5x − 3x
2
.
11. u
t
= a
2
u
xx
+ 2t
2
, 0 < x < 1, t > 0,
u(0, t) = t, u(1, t) = 2t,
u(x, 0) = 2sinπx − sin3πx.
12. u
t
= a
2
u
xx
+ t, 0 < x < 1, t > 0,
u
x
(0, t) = 2t, u(1, t) = 1,
u(x, 0) = 1 + 2cos
5π
2
x.
13. u
t
= a
2
u
xx
+ 2xt, 0 < x < 1, t > 0,
u(0, t) = 2t, u
x
(1, t) = 1,
u(x, 0) = x − 2sin
3π
2
x.
14. u
t
= u
xx
+ 3t − 1, 0 < x < 1, t > 0,
u
x
(0, t) = 2, u
x
(1, t) = 2,
u(x, 0) = 1 + 2x − 2cos3πx.
15
 3. ut = a2 uxx + 2x + 1, 0 < x < 1, t > 0,
    u(0, t) = 1, ux (1, t) = 2,
    u(x, 0) = 2x + 1.

 4. ut = a2 uxx + x + 1, 0 < x < 1, t > 0,
    u(0, t) = 0, u(1, t) = 1,
    u(x, 0) = x.

 5. ut = a2 uxx + 2x + 1, 0 < x < 1, t > 0,
    ux (0, t) = 2, u(1, t) = 1,
    u(x, 0) = 2x − 1.

 6. ut = a2 uxx + x + 2, 0 < x < 1, t > 0,
    u(0, t) = 0, ux (1, t) = 1,
    u(x, 0) = x.

 7. ut = a2 uxx + t, 0 < x < 1, t > 0,
    u(0, t) = 2t, u(1, t) = 1,
    u(x, 0) = x − 3sin2πx.

 8. ut = a2 uxx + 2xt, 0 < x < 1, t > 0,
    ux (0, t) = −1, u(1, t) = t,
    u(x, 0) = 1 − x − cos 7π2
                              x.

 9. ut = a2 uxx + 2t3 , 0 < x < 1, t > 0,
    u(0, t) = 1, ux (1, t) = 2t,
    u(x, 0) = 1 + sin 5π 2
                           x.

10. ut = uxx + t2 − 1, 0 < x < 1, t > 0,
    ux (0, t) = 5, ux (1, t) = −1,
    u(x, 0) = 2 + 5x − 3x2 .

11. ut = a2 uxx + 2t2 , 0 < x < 1, t > 0,
    u(0, t) = t, u(1, t) = 2t,
    u(x, 0) = 2sinπx − sin3πx.

12. ut = a2 uxx + t, 0 < x < 1, t > 0,
    ux (0, t) = 2t, u(1, t) = 1,
    u(x, 0) = 1 + 2cos 5π 2
                            x.

13. ut = a2 uxx + 2xt, 0 < x < 1, t > 0,
    u(0, t) = 2t, ux (1, t) = 1,
    u(x, 0) = x − 2sin 3π 2
                            x.

14. ut = uxx + 3t − 1, 0 < x < 1, t > 0,
    ux (0, t) = 2, ux (1, t) = 2,
    u(x, 0) = 1 + 2x − 2cos3πx.




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