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PDE Differentiating Integrals

  1. Apr 8, 2008 #1
    1. The problem statement, all variables and given/known data

    U is a function of x and t

    d/dt(U) = d/dx(U) + V(x,t)U
    U(x,0) = f(x)

    Suppose:
    U(x,t) = e^(Integral from 0 to 1 [V(x+s,t-s)]ds) * f(x+t)

    Show directly (no change of variables) that this solves the above PDE
    Show using change of variables that this solves the above PDE letting
    Alpha = x+t
    Gamma = x-t

    3. The attempt at a solution

    My main question is how to evlauate d/dt { Integral from 0 to 1 [V(x+s,t-s)]ds }
     
  2. jcsd
  3. Apr 8, 2008 #2

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Use the Liebniz integral rule, described in these articles at wikipedia and mathworld.
     
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