I'm confused about the superposition when the B.C(boundary condition) is continuity condition between two domain.(adsbygoogle = window.adsbygoogle || []).push({});

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

∂^{2}A/∂r^{2}+ 1/r ∂A/∂r + 1/r^{2}∂^{2}A/∂θ^{2}= 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 : A_{1}(b,θ)=A_{2}(b,θ) , and etc.. on elsewhere(r=a, or θ=somewhere)

2. (b<r<c, 0<θ<2pi)

with B.C : ∂A_{1}/∂θ=∂A_{2}/∂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,

A_{1}(r,θ)=A_{11}(r,θ)+A_{12}(r,θ) (1)

that,

A_{11}(r,θ) satisfy A_{11}(b,θ)=0 (2)

A_{12}(r,θ) satisfy A_{12}(b,θ)=A_{2}(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

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# Superposition on continuty condition

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