= Negative-diffusion criterion for viscous disk instability
{title2=$\partial_\Sigma(\bar\nu\Sigma)<0$}
Freezing coefficients locally in the <Keplerian viscous diffusion equation> gives $\Sigma_{1,t}\simeq3\partial_\Sigma(\bar\nu\Sigma)\Sigma_{1,rr}$. A radial <Fourier mode> grows at rate $-3\partial_\Sigma(\bar\nu\Sigma)k_r^2$. Negative response reverses ordinary smoothing and gives a <backward heat equation>, within the <wavelength> range where the <thin disc> transport closure applies.
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