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Marshak Wave.

  1. Apr 17, 2010 #1


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    I have this PD equation:
    T_t=\nabla ^2 T^4
    where T=T(r,t) the above laplacian is spherical symmetrical (i.e only the spherical radial coordinate of the operator should be taken into account).
    and [tex]Q_0=\int_{0}^{\infty}T(r,t=0)dr[/tex].

    So I tried solving it by seperation of variables but I get a tough ODE of the radial part.

    Here's what I got
    [tex]T(r,t)=F(r)G(t) \newline \frac{\frac{dG}{dt}}{G^4}=\frac{\nabla ^2 F^4}{F}=\lambda [/tex]
    Now after some manipulations I get for the radial equation the next equation:

    And this is where I am stuck, any suggestion as to how to untie this equation, is even possible?
  2. jcsd
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