Solving specific PDE

stanley.st

Hello,

I derived a model in the form

[tex]\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}[/tex]

I don't know to solve that.

THanks for help.

Eynstone

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

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stanley.st	Solving specific PDE Hello, I derived a model in the form [tex]\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}[/tex] I don't know to solve that. THanks for help.

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