1. Not finding help here? Sign up for a free 30min 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!

Very weird PDE problem

  1. Sep 30, 2007 #1

    nicksauce

    User Avatar
    Science Advisor
    Homework Helper

    The question is:

    Write a short paragraph that physical problem modeled by the equation:

    [tex]
    \frac{\partial{U}}{\partial{t}} = \frac{1}{4}\frac{\partial^2{U}}{\partial^2{x}} -12[U - 8x][/tex]

    Subject to
    IC: U(x,0) = 3x
    BCs: U(0,t) =0, u(2,t) = 2t

    Okay so clearly, the physical problem is some kind of heat problem with a one dimensional rod and a heat source term. However, the problem is that the IC and the BCs are conflicting, since U(2,0) = 6, from the IC, but U(2,0) = 0 from the BC. Any advice to go about answering this?
     
  2. jcsd
  3. Oct 3, 2007 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What that means is that your function is not continuous. That's alright if you are using integration techniques which will "smooth" the discontinuity. I would recommend using a Fourier series solution. In fact, I would write V(x,t)= U(x,t)- 2t and solve the problme for V so that the boundary conditions are "homogeneous" and you can use a Fourier sine series.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Very weird PDE problem
  1. PDE problem (Replies: 1)

  2. PDE problem (Replies: 0)

  3. PDE problem (Replies: 1)

  4. A very Weird Integral (Replies: 8)

Loading...