Stuck with a solution for LSE

1. Apr 1, 2014

soni

Hi,
I am looking for a solution of

$\frac{\partial\phi}{\partial t} = |\nabla\phi|div\left(\frac{\nabla\phi}{|\nabla\phi|}\right)$

in the form of

$\phi (x_1,x_2,t)=\gamma (t)\sqrt{x_1^2+x_2^2}-\alpha (t)$

i got myself to, where i want to evaluate $\gamma, \alpha$

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

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