# Superposition on continuty condition

1. Jan 15, 2012

### smoger

I'm confused about the superposition when the B.C(boundary condition) is continuity condition between two domain.

The laplace equation(or possion) expressed as (in circular annulus),

2A/∂r2 + 1/r ∂A/∂r + 1/r22A/∂θ2 = f(r,θ)

Assume that there are two domains where the boundary of each domain is :

1. (a<r<b, 0<θ<2pi)
with B.C : A1(b,θ)=A2(b,θ) , and etc.. on elsewhere(r=a, or θ=somewhere)

2. (b<r<c, 0<θ<2pi)
with B.C : ∂A1/∂θ=∂A2/∂θ (at r=b)
, and etc.. on elsewhere(r=c, or θ=somewhere)

Is that right to solve the equation by adopting super position theory?
for example, In domatin 1,

A1(r,θ)=A11(r,θ)+A12(r,θ) (1)

that,
A11(r,θ) satisfy A11(b,θ)=0 (2)

A12(r,θ) satisfy A12(b,θ)=A2(b,θ) (3)

Can i make the continuty condition 0 as a general non homogeneous B.C condition to solve the equation by
super position? thx in advance

Last edited: Jan 15, 2012
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