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Stuck with a solution for LSE

  1. Apr 1, 2014 #1
    I am looking for a solution of

    [itex]\frac{\partial\phi}{\partial t} = |\nabla\phi|div\left(\frac{\nabla\phi}{|\nabla\phi|}\right)[/itex]

    in the form of

    [itex]\phi (x_1,x_2,t)=\gamma (t)\sqrt{x_1^2+x_2^2}-\alpha (t)[/itex]

    i got myself to, where i want to evaluate [itex]\gamma, \alpha[/itex]

    [itex]\dot{\gamma}(t)\sqrt{x_1^2+x_2^2} - \dot{\alpha}(t)=\frac{1}{\sqrt{x_1^2+x_2^2}}.[/itex]

    Anyone having an idea how to do this, or am i missing something? It's been a while since i last used PDE so this is as far as i got.
    any kind of help is appreciated
  2. jcsd
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