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Homework Help: Diffusion equation

  1. Feb 24, 2016 #1
    1. The problem statement, all variables and given/known data
    Hello, I don't understand the solution of an exercise

    Let P(x) be a continuous function such that |P(x)|≤Ceax² .
    Show that formula (8) for the solution of the diffusion equation makes sense for 0 < t < 1/(4ak), but not necessarily for larger t.

    2. Relevant equations
    Equation (8) refers to
    u(x,t)=1/√(4*pi*k*t) ∫ e-(x-y)²/4ktP(y) dy
    3. The attempt at a solution
    The solution just says that

    I don't understand how they conclude ? I don't see why we have 0 < t < 1/(4ak)

  2. jcsd
  3. Feb 24, 2016 #2


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    Consider the sign of the ##y^2## term in the exponent. What has to be true for the integral to converge?
  4. Feb 25, 2016 #3
    I see, thanks !
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