Контрольные работы по уравнениям математической физики. Ковтанюк А.Е. - 16 стр.

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15. u
t
= a
2
u
xx
+ 3t, 0 < x < 1, t > 0,
u(0, t) = 1, u(1, t) = t,
u(x, 0) = 1 − x + sin4πx.
16. u
t
= a
2
u
xx
+ 2xt, 0 < x < 1, t > 0,
u
x
(0, t) = 2t, u(1, t) = t,
u(x, 0) = 4cos
3π
2
x.
17. u
t
= a
2
u
xx
+ t
2
, 0 < x < 1, t > 0,
u(0, t) = t, u
x
(1, t) = 2t,
u(x, 0) = 4sin
9π
2
x.
18. u
t
= u
xx
+ 2t, 0 < x < 1, t > 0,
u
x
(0, t) = 3, u
x
(1, t) = 1,
u(x, 0) = 1 + 3x − x
2
.
19. u
t
= a
2
u
xx
+ 2t, 0 < x < 1, t > 0,
u(0, t) = t
2
, u(1, t) = 1,
u(x, 0) = x − sinπx + 2sin5πx.
20. u
t
= a
2
u
xx
+ t, 0 < x < 1, t > 0,
u
x
(0, t) = 2, u(1, t) = t
2
,
u(x, 0) = 2x − 2 + cos
5π
2
x.
21. u
t
= a
2
u
xx
+ x + t, 0 < x < 1, t > 0,
u(0, t) = 2t
2
, u
x
(1, t) = t,
u(x, 0) = sin
π
2
x − 3sin
3π
2
x.
22. u
t
= u
xx
+ t − 2, 0 < x < 1, t > 0,
u
x
(0, t) = 0, u
x
(1, t) = 2,
u(x, 0) = 1 + x
2
− cos3πx + 2cos4πx.
23. u
t
= a
2
u
xx
− 2x + 2, 0 < x < 1, t > 0,
u(0, t) = 2t, u(1, t) = t
2
,
u(x, 0) = sin2πx − 2sin3πx.
24. u
t
= a
2
u
xx
+ tx − 1, 0 < x < 1, t > 0,
u
x
(0, t) = t
2
, u(1, t) = 1,
u(x, 0) = 1 − cos
π
2
x .
25. u
t
= a
2
u
xx
+ 5xt, 0 < x < 1, t > 0,
u(0, t) = 1, u
x
(1, t) = 2t
2
,
u(x, 0) = 1 + sin
5π
2
x.
26. u
t
= u
xx
+ 2t
2
+ 3, 0 < x < 1, t > 0,
u
x
(0, t) = 2, u
x
(1, t) = 0,
u(x, 0) = 2 + 2x − x
2
− 4cos2πx.
16
15. ut = a2 uxx + 3t, 0 < x < 1, t > 0,
    u(0, t) = 1, u(1, t) = t,
    u(x, 0) = 1 − x + sin4πx.

16. ut = a2 uxx + 2xt, 0 < x < 1, t > 0,
    ux (0, t) = 2t, u(1, t) = t,
    u(x, 0) = 4cos 3π2
                       x.

17. ut = a2 uxx + t2 , 0 < x < 1, t > 0,
    u(0, t) = t, ux (1, t) = 2t,
    u(x, 0) = 4sin 9π2
                       x.

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

19. ut = a2 uxx + 2t, 0 < x < 1, t > 0,
    u(0, t) = t2 , u(1, t) = 1,
    u(x, 0) = x − sinπx + 2sin5πx.

20. ut = a2 uxx + t, 0 < x < 1, t > 0,
    ux (0, t) = 2, u(1, t) = t2 ,
    u(x, 0) = 2x − 2 + cos 5π 2
                                  x.

21. ut = a2 uxx + x + t, 0 < x < 1, t > 0,
    u(0, t) = 2t2 , ux (1, t) = t,
    u(x, 0) = sin π2 x − 3sin 3π2
                                   x.

22. ut = uxx + t − 2, 0 < x < 1, t > 0,
    ux (0, t) = 0, ux (1, t) = 2,
    u(x, 0) = 1 + x2 − cos3πx + 2cos4πx.

23. ut = a2 uxx − 2x + 2, 0 < x < 1, t > 0,
    u(0, t) = 2t, u(1, t) = t2 ,
    u(x, 0) = sin2πx − 2sin3πx.

24. ut = a2 uxx + tx − 1, 0 < x < 1, t > 0,
    ux (0, t) = t2 , u(1, t) = 1,
    u(x, 0) = 1 − cos π2 x .

25. ut = a2 uxx + 5xt, 0 < x < 1, t > 0,
    u(0, t) = 1, ux (1, t) = 2t2 ,
    u(x, 0) = 1 + sin 5π 2
                           x.

26. ut = uxx + 2t2 + 3, 0 < x < 1, t > 0,
    ux (0, t) = 2, ux (1, t) = 0,
    u(x, 0) = 2 + 2x − x2 − 4cos2πx.




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