Solving specific PDE

1. Oct 1, 2011

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.

2. Oct 3, 2011

Eynstone

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