sr004

∂2u

∂2u

∂2u

∂2u

1 ∂ u

1 ∂2 u

+

+

=

+

+

.

∂ x

2

∂ y

2

∂ z

2

∂r

2

r ∂r

r ∂ϕ

2

∂ 2u

+

1

∂ u

+

1 ∂ 2 u

= 0 .

(81)

∂r

2

r

∂r

r

∂ϕ

2

K1 : x2 + y 2 = R12 K2 : x2 + y2 = R22

:

u(R1;ϕ =)u1, u R2 ;ϕ (= u2 .

(82)

∂2u

+

1 ∂ u

= 0 .

∂r

2

r ∂r

, :

u = 1 ln r + C2 .

(83)

1 2 (82):

u1 = 1 ln R1 + C2 , u2 = 1 ln R2 + C2 .

:

u2 − u1

u2 ln R2 − u1 ln R1

=

,

2

=

.

1

ln

R2

ln

R2

R1

R1

1 2 (83), :

u

2

ln

r

− u ln

r

u =

R1

1

R2

.

R2

ln

R1