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PDE problem : diffusion equation! help!

  1. Sep 27, 2006 #1
    Hi all,

    I am stuggling with this question ...

    http://img86.imageshack.us/img86/2662/picture6fb5.png [Broken]

    so far i have only tried part (a), but since i can't see how to do that so far... :(

    ok so what to do...

    do we first look at an 'associated problem' ? ... something like

    http://img245.imageshack.us/img245/4544/picture7vu3.png [Broken]

    lol, this stuff is all quite confusing :confused:

    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Sep 27, 2006 #2
    hmm ok i tryed some more and i come up with this answer:

    http://img301.imageshack.us/img301/3903/picture8cm8.png [Broken]

    however i don't know how to simplify it from here, i have looked up integral tables and still no luck. any suggestions guys? lol assuming the answer is right in the first place! :P

    Last edited by a moderator: May 2, 2017
  4. Sep 28, 2006 #3
    i think you can solve these by separation of variables that is

    assume u(x,t) is a product of two functions - one which depends on x, and one which depends on t
    maybe something like this u(x,t) = F(x) G(t)

    and solve from there
    your text should give a description of doing such a problem...
  5. Sep 29, 2006 #4
    hmm i can't seem to get seperation of variables to work... what do you reckon for part (b)?
  6. Sep 29, 2006 #5


    User Avatar

    For part (b), you need to reduce the nonhomogenous boundary condition problem to a homogeneous one.
  7. Sep 29, 2006 #6
    ok, that sounds like a good idea.... but how do i go about doing that ? a hint please ;)

    also, what do you think of my answer for part (a)?
    Last edited: Sep 29, 2006
  8. Sep 29, 2006 #7
    hmm ok let me see.. what about if we let w(x,t) = exp(-x)

    then u(x,t) = w(x,t) + v(x,t)

    then v(x,t) satifies: http://img227.imageshack.us/img227/7427/picture10zn8.png [Broken]

    so then we have to solve that pde problem? :S
    Last edited by a moderator: May 2, 2017
  9. Sep 30, 2006 #8
    its cool guys i worked it out! :D yay
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