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PDE:Cauchy Problem for Heat Equation

  1. Sep 26, 2013 #1
    1. The problem statement, all variables and given/known data
    Solve the Cauchy problem
    ut =kuxx, x ∈ R, t>0, u(x, 0) = φ(x),
    for the following initial conditions.
    (a) φ(x)=1if |x|<1 and φ(x)=0 if |x|>1.
    Write the solutions in terms of the erf function.

    2. Relevant equations
    u(x,t)=∫G(x-y,t)*φ(y)dy from -∞, to ∞
    where G(x,t) is the heat kernel or fundamental solution to heat equation.

    3. The attempt at a solution
    I am not sure if this correct:
    Separate the integral into different parts according above condition and then plugin φ(x) value for φ(y) in the integral. And then proceed from there on
  2. jcsd
  3. Sep 27, 2013 #2


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    Sounds good to me. Just do it!
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