Гургула, Мойсишин "Розрахи з матана",

1

r

2

u(r , 0)=

1

−

,

8

13

∂u(r , 0)

= 0 ,

u(13, t)= 0 .

∂t

8.14.

∂2u

=14

u ,

0 ≤ r <12 ,

0 < t < ∞ ,

∂t2

1

r

2

u(r , 0)=

1

−

,

8

12

∂u(r , 0)

= 0 ,

u(12, t)= 0 .

∂t

8.15.

∂2u

=15

u ,

0 ≤ r <11 ,

0 < t < ∞ ,

∂t2

1

r 2

u(r , 0)=

1

−

,

8

11

∂u(r , 0)

= 0 ,

u(11, t)= 0 .

∂t

8.16.

∂2u

=16

u ,

0 ≤ r <10 ,

0 < t < ∞ ,

∂t2

1

r 2

u(r , 0)=

1

−

,

8

10

∂u(r , 0)

= 0 ,

u(10, t)= 0 .

∂t

8.17.

∂2u

=17

u ,

0 ≤ r < 9 ,

0 < t < ∞ ,

∂t2

1

r 2

u(r , 0)=

1

−

,

8

9

∂u(r , 0)

= 0 ,

u(9, t)= 0 .

∂t

1

r 2

u(r , 0)=

1

−

,

8

4

=

0 ,

u(4, t)= 0 .

∂u(r , 0)

∂t

8.23.

∂2u

= 23

u ,

0 ≤ r < 3 ,

0 < t < ∞ ,

∂t

2

1

r 2

u(r , 0)=

1

−

,

8

3

= 0 ,

u(3, t)= 0 .

∂u(r , 0)

∂t

8.24.

∂2u

= 24

u ,

0 ≤ r < 2 ,

0 < t < ∞ ,

∂t

2

1

r 2

u(r , 0)=

1

−

,

8

2

=

0 ,

u(2, t)= 0 .

∂u(r , 0)

∂t

8.25.

∂2u

= 25

u ,

0 ≤ r <1 ,

0 < t < ∞ ,

∂t

2

1

[1 − r2 ],

u(r , 0)=

8

∂u(r , 0)

u(1, t)= 0 .

∂t

= 0 ,

8.26.

∂2u

= u ,

0 ≤ r < 6 ,

0 < t < ∞ ,

∂t

2

1

r 2

u(r , 0)=

1 −

,

8

6

= 0 ,

u(6, t)= 0 .

∂u(r , 0)

∂t

2x

2

,

0 ≤ x ≤

3

,

u(0, t)=

0 ,

u(x, 0)=

3

2

0 .

3

u(3, t)=

3 − x ,

< x

≤ 3 ,

2

9.2.

∂u

=

∂2u

,

0 < x < 2 ,

t > 0 ,

∂t

∂x2

u(0, t)= 0 ,

u(x, 0)=

x2

,

0 ≤ x ≤ 1 ,

2 − x , 1 < x ≤ 2 ,

u(2, t)= 0 .

9.3.

∂u

=

25

∂2u

,

0 < x < 5 ,

t > 0 ,

∂t

∂x2

2x

2

,

0 ≤ x ≤

5

,

u(0, t)= 0 ,

u(x, 0)=

5

2

5

u(5, t)= 0 .

5 − x ,

< x ≤ 5 ,

2

9.4.

∂u

=

16

∂2u

,

0 < x < 4 ,

t > 0 ,

∂t

∂x2

x

2

,

0 ≤ x ≤ 2 ,

u(0, t)= 0 ,

u(x, 0)=

2

u(4, t)= 0 .

4 − x , 2 < x ≤ 4 ,

9.5.

∂u

=

4

∂2u

,

0 < x < 5 ,

t > 0 ,

∂t

∂x2

2x

2

,

0 ≤ x ≤

5

,

u(0, t)= 0 ,

u(x, 0)=

5

2

5

u(5, t)= 0 .

5 − x ,

< x

≤

5 ,

2

9.6.

∂u

=

∂2u

,

0 < x < 3 ,

t > 0 ,

∂t

∂x2

2x

2

,

0 ≤ x ≤

3

,

u(0, t)= 0 ,