= Diffusion from a gradient energy
{title2=$E(u)=\int\Phi(|\nabla u|)$}
The formal $L^2$ <gradient flow> of this energy is $u_t=\operatorname{div}(\Phi'(r)\nabla u/r)$, with a <Neumann boundary condition> for no flux. The radial Hessian eigenvalues of the gradient integrand are $\Phi''(r)$ and $\Phi'(r)/r$. Their signs distinguish convex forward diffusion from formal backward diffusion. The <heat equation> uses $\Phi(r)=r^2/2$, whereas <total variation flow> uses $\Phi(r)=r$ with a <subgradient> interpretation at zero.
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