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∂v(s,n)/∂n + ∂u(s,n)/∂s + ∂ξ(s,n)/∂s + An dc(s)/ds = 0 (1)

A1 ∂ξ(s,n)/∂n + ∂v(s,n)/∂s -c(s)+A2 v(s,n) + A3 c(s) = 0 (2)

∂u(s,n)/∂s + 2A2 u(s,n)=A2(ξ(s,n) + Anc(s)) -A1 ∂ξ(s,n)/∂s-A2nc(s) (3)

Unknowns: u(s,n),v(s,n),ξ(s,n)

Boundary conditions: v(s,1)=v(s,-1)= 0

I am trying to solve this set of PDEs by iteration and I am not sure if I am going about it the correct way. I have attached my attempt at a solution and it seems i am going in circles. Does anyone have a better idea? Someone suggested using Fourier analysis to solve the problem. I am reading that up now but i would really appreciate any ideas on how to start.

Thank you.

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# Help with linear PDE problem

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