Solving specific PDE

  1. 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.
     
  2. jcsd
  3. This looks like the heat equation.So, I suggest seperating variables.
     
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