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!

Heat Equation Time dependant heat loss

  1. Nov 2, 2008 #1


    User Avatar

    1. The problem statement, all variables and given/known data
    Solve the heat equation: [tex]u_{t} = u_{xx} - u - x*e^{-t}[/tex]
    BC: u(0,t) = 0, u(1,t) = 0
    IC: u(x,0) = x

    2. Relevant equations

    3. The attempt at a solution

    The only progress I've made so far is figuring out that the steady state solution is zero. Other than that I don't know where to start with the time dependent solution. Basically I could use some help starting this problem, thanks!
  2. jcsd
  3. Nov 3, 2008 #2


    User Avatar
    Homework Helper
    Gold Member

    Try finding functions [itex]f(t)[/itex] and [itex]g(x)[/itex] such that [itex]w(x,t) \equiv f(t)u(x,t)+g(x)[/itex] satisfies the homogeneous heat equation [itex]w_t=w_{xx}[/itex]...then use your boundary conditions for u(x,t) to find corresponding BCs for w(x,t) and solve for w(x,t) and use that to find u(x,t).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Heat Equation Time dependant heat loss
  1. Heat equation (Replies: 2)

  2. Heat Equation (Replies: 1)

  3. Heat equation (Replies: 2)

  4. The heat equation (Replies: 17)