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Heat Equation Time dependant heat loss

  1. Nov 2, 2008 #1


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    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


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    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).
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