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Inhomogeneous heat equation integral solution

  1. Apr 18, 2013 #1
    1. The problem statement, all variables and given/known data
    I have been given the following expression for the general solution to the inhomogeneous heat equation, with inhomog b.c. and i.c.

    i have two questions, does anyone know where i found find this in a text book? i have search only for ages and people only really solve homogeneous cases, or one inhomog and the other homog, which makes it easier.

    if not, how do the boundary conditions come into the third integral of this equation?

    there's u(r',t') and du/dn (r',t') in this term

    making up an example, lets say u(0,t) = f(t)

    how is this used in the third term of the integral?

    to me it looks like it isn't incorporated in at all

    2. Relevant equations

    http://img803.imageshack.us/img803/7266/asax.jpg [Broken]

    [c]

    is it that the normal derivatives in the G and u make the integral be evaluated at r=0 ?

    so u(r',t') -> u(0,t')
    du/dn (r',t') = du/dr (0,t') is that right?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
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