How Do You Solve a PDE Model Similar to the Heat Equation?

[stanley.st]

Hello,

I derived a model in the form

\begin{array}{rcl}\frac{\partial U(\vec{x},t)}{\partial t}&=&\gamma^2\Vert\nabla U(\vec{x},t)\Vert,\\\int_{\Omega}U(\vec{x},t)\, d \Omega&=&U_0,\quad\forall t\\U(\vec{x},0)&=&f(\vec{x}).\end{array}

I don't know to solve that.

THanks for help.

 

[Eynstone]

This looks like the heat equation.So, I suggest seperating variables.