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Marshak Wave.

  1. Apr 17, 2010 #1

    MathematicalPhysicist

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    Gold Member

    I have this PD equation:
    [tex]
    T_t=\nabla ^2 T^4
    [/tex]
    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:
    [tex]F''(r)+3(F'(r))^2/F(r)+2F'(r)/r-\lambda/(2F(r))^2=0[/tex]

    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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