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What is the PDE called where the rate of change is proportional to the velocity/gradient information?

$\frac{\partial\phi}{\partial t}=kV$, where $k$ is a constant and $V$ is the velocity.

According to wiki, it seems like Advection equation (The advection equation is the partial differential equation that governs the motion of a conserved scalar field as it is advected by a known velocity vector field). But the PDE isn't exactly what I am looking for.

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Could you explain the relation between $\phi$ and $V$ in your equation? –  user53153 Jan 18 '13 at 1:57
    
$V$ is the gradient of a function $f$ which depends on $\phi$. –  John Smith Jan 18 '13 at 5:12

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