1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook