Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Verifying Kirchhoff formula

  1. Jun 21, 2016 #1
    I've read the derivation of Kirchhoff's formula for three dimensional wave equation using the Euler-Poisson-Darboux equation. The derivation seems to be fine, but I thought that the Kirchhoff's formula as a final result is a kind of result that you should be able to verify it by substituting it back to the wave equation. Well I substituted it into the wave equation, and tried to manipulate the expressions in hope of all the terms cancelling, but I couldn't make it work. My question is that has anyone ever succeeded in verifying the Kirchhoff's formula by substituting it into the wave equation?

    The wave equation:

    [tex]
    \partial_t^2u(t,x) - \nabla_x^2u(t,x) = 0
    [/tex]

    The Kirchhoff's formula:

    [tex]
    u(t,x) = \frac{1}{4\pi t^2}\int\limits_{\partial B(x,t)} \big(t\partial_tu(0,y) + u(0,y) + (y-x)\cdot\nabla_xu(0,y)\big)d^2y
    [/tex]
     
  2. jcsd
  3. Jun 26, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Verifying Kirchhoff formula
  1. Kirchhoff Transform (Replies: 0)

Loading...