= Solution
Let $F(\Sigma)=\nu(\Sigma)\Sigma$ and perturb the homogeneous state by $\delta\Sigma\propto e^{st+ikx}$. Linearization gives
$$
s\delta\Sigma=3F'(\Sigma_0)\partial_x^2\delta\Sigma,
\qquad
\boxed{s=-3k^2\left.\frac{d(\nu\Sigma)}{d\Sigma}\right|_{\Sigma_0}}.
$$
Thus $d(\nu\Sigma)/d\Sigma<0$ produces the <viscous instability of an accretion disk>: a density enhancement transports angular momentum less effectively, loses material more slowly, and grows. The ring separates into denser narrow ringlets and lower-density gaps until nonlinear effects regularize the backward diffusion.
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