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Find the Equilibrium temperature distribution of a PDE

  1. Jun 12, 2013 #1
    1. The problem statement, all variables and given/known data

    1) What is the Equilibrium temperature distributions if α > 0?
    2) Assume α > 0, k=1, and L=1, solve the PDE with initial condition u(x,0) = x(1-x)

    2. Relevant equations

    du/dt = k(d^2u/dx^2) - (α*u)

    3. The attempt at a solution

    I got u(x) = [(α*u*x)/2k]*[x-L] for Part#1 but this was told to be wrong

    Part #2 I got α*u = -2, Also wrong.

    Any insight how to correct this?
     
  2. jcsd
  3. Jun 13, 2013 #2
    With the equilibrium condition you should just have a ODE.

    [tex]\frac{d^2u}{dx^2}-\frac{a}{k}u=0[/tex]
     
  4. Jun 13, 2013 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, it certainly is! How did you get that function?

    An "equilibrium" solution is one that no longer changes: du/dt= 0 so the partial differential equation becomes k d^2u/dx^2- au= 0, a linear, homogeneous, second order, ordinary differential equations. If you are taking a course in "partial differential equations", you certainly should know how to solve such an equation.
     
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