Solving specific PDE

by stanley.st
Tags: solving, specific
 P: 31 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.
 P: 336 This looks like the heat equation.So, I suggest seperating variables.

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