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A Yet another Poisson-Botzmann case

  1. Aug 19, 2017 #1
    Hello,

    I'm trying to find either an analytical or a semi-analytical method for solving the following P-B Eq.
    upload_2017-8-19_20-15-16.png
    with C and A being two constants. The equation is to be solved within a rectangle with constant boundary conditions.

    If anyone has a clue, I'll be grateful.

    Have a good evening.
     

    Attached Files:

  2. jcsd
  3. Aug 20, 2017 #2
    Have you tried using a Fourier transform? The exponential in your equation makes that method seem promising.
     
  4. Aug 20, 2017 #3
    Not sure that you're right because the exponential term contains the function itself rather than the independent variables x or y.
     
  5. Aug 20, 2017 #4
    In that case, the only other method I know would be to write the right hand side as a power series centered at the origin of the domain and truncate the series to some low order, like first or second, and solve the resulting PDE.
     
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