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Laplacian-like equation

  1. Feb 2, 2012 #1
    Hi All,

    I try to solve second order PDE:
    [itex] \frac{\partial^2 f(x,y)}{\partial x^2}=-a^2f(x,y) [/itex]
    [itex] \frac{\partial^2 f(x,y)}{\partial y^2}=-a^2f(x,y) [/itex]
    where [itex] a >2[/itex], [itex] f(x,y)[/itex] is a periodic function in x, but has fixed boundaries in y.

    Is there a way to solve it? What does the solution look like? Any hints or references are welcome. thanks a lot!
    Last edited: Feb 2, 2012
  2. jcsd
  3. Feb 3, 2012 #2


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    Gold Member

    I'm also learning PDE's so take what I say with a grain of salt.
    From my experience one needs to describe the region of where the PDE is evaluated/calculated. Also, telling us what are the "fixed boundaries in y" is also very important.
    Edit: Your equations read [itex]\nabla ^2 f = -2a^2 f[/itex] where f depends on 2 spatial variables x and y.
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