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Question: Solving a PDE analytically with a boundary condition.

Question:Solving a PDE analytically with a boundary condition.

Jamie128 165 Maple 2022
pde pdsolve differential-equations boundary-conditions
September 16 2023
0

I wanted to solve a pde of two variables in spherical coordinates with a boundary condition at a specific radius. I am doing something wrong because the pdsolve just evaluates for several minutes and does not actually give anything.

Could someone have a look and let me know what I am doing wrong.

> 

restart
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``
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with(Physics[Vectors])
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Setup(mathematicalnotation = true)

[mathematicalnotation = true]

 (1)
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eq3 := Laplacian(Phi_out(r, theta)) = 0

((r^2*(diff(diff(Phi_out(r, theta), r), r))+2*r*(diff(Phi_out(r, theta), r))+diff(diff(Phi_out(r, theta), theta), theta))*sin(theta)+(diff(Phi_out(r, theta), theta))*cos(theta))/(r^2*sin(theta)) = 0

 (2)
> 

bc1 := eval(Phi_out(r, theta)-Omega*mu*(-1+cos(2*theta))/(2*r), r = R) = 0

Phi_out(R, theta)-(1/2)*Omega*mu*(-1+cos(2*theta))/R = 0

 (3)
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``
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pdsolve([eq3, bc1])
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NULL

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