## Laplace equation with boundary condition

Good afternoon,

I am a PhD student in motions of damaged ships. I am trying to find a solution of Laplace equation inside a box with a set of boundary conditions such that:

2$\phi$=0
$\phi$x=1 when x=-A and x=A
$\phi$y=0 when y=-B and y=B
$\phi$z=0 when z=Ztop and z=Zbot

I have tried different solutions that look like
$\phi$=x+Ʃ(cos(α(x+A))cos(β(y+B))cosh(γ(z-Ztop))

α=n*PI/A n=1...∞
β=m*PI/B m=1...∞
and α222

I can't find a solution that satisfy everything.
I either satisfy the boundary conditions or Laplace equation but not both.
The problem comes from the need to have a sinh(z)=0 for 2 values...
I can't figure out how to go around the problem.

Any advice would be really nice.

Thanks
Anne

PS: I have the three permutation to find $\phi$x=1 then $\phi$y=1 and $\phi$z=1
I have the same problem in the three cases.
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 Quote by ACG_PhD Good afternoon, I am a PhD student in motions of damaged ships. I am trying to find a solution of Laplace equation inside a box with a set of boundary conditions such that: ∇2$\phi$=0 $\phi$x=1 when x=-A and x=A $\phi$y=0 when y=-B and y=B $\phi$z=0 when z=Ztop and z=Zbot I have tried different solutions that look like $\phi$=x+Ʃ(cos(α(x+A))cos(β(y+B))cosh(γ(z-Ztop)) α=n*PI/A n=1...∞ β=m*PI/B m=1...∞ and α2+β2=γ2 I can't find a solution that satisfy everything. I either satisfy the boundary conditions or Laplace equation but not both. The problem comes from the need to have a sinh(z)=0 for 2 values... I can't figure out how to go around the problem. Any advice would be really nice. Thanks Anne PS: I have the three permutation to find $\phi$x=1 then $\phi$y=1 and $\phi$z=1 I have the same problem in the three cases.
Try x+c as the solution

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