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Solving the heat equation on the real line using fourier transforms

  1. Nov 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Solve the heat equation
    [itex]\frac{∂}{∂t}[/itex]u[itex](x,t)[/itex]=[itex]\frac{1}{α^2}[/itex][itex]\frac{∂^2}{∂t^2]}[/itex]u(x,t)

    on the real line ℝ with the initial conditions:
    u(x,0)= 1 if |x| [itex]\leq[/itex]1, 0 for any other value of x


    2. Relevant equations

    I don't even know where to start for this question, but I believe that I will have to use a fourier transform, and perhaps separation of variables, to find a solution to this problem



    3. The attempt at a solution

    I don't even know where to start.
     
    Last edited: Nov 23, 2011
  2. jcsd
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