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Solving non-homogeneous PDE (unsure of methodology)

  1. Dec 1, 2011 #1
    1. The problem statement, all variables and given/known data

    [tex]u_{t} = ku_{xx}[/tex]
    [tex]u_{x}(0, t) = 0[/tex]
    [tex]u_{x}(L, t) = B =/= 0[/tex]
    [tex]u(x, 0) = f(x)[/tex]


    2. Relevant equations



    3. The attempt at a solution

    I believe that no equilibrium solution exists because we can't solve
    [tex]u_{xx} = 0[/tex]
    with our boundary conditions. I'm a little lost as to where to take this question from here.

    Been trying to work with this question for around 30 minutes now, I'm lost. :D
     
  2. jcsd
  3. Dec 1, 2011 #2
    Think I figured it out now, derp...

    I just chose a reference function
    [tex]r(x, t) = r(x) = c_{1}\frac{x^2}{2}[/tex]
    and solved for c1 which allowed me to generate a new linear homogeneous PDE and summed up the solution and the reference function to find the final solution. Would be nice if someone replied that I used the correct method though! Thanks!
     
  4. Dec 1, 2011 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes. Find a function that satisfies the boundary conditions with regard to the differential equation, then subtract it off to get a new differential equation with homogeneous boundary conditions.
     
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