  Reaction-nonlinear diffusion partial differential equations can exhibit
shock-fronted travelling wave solutions. Prior work by Yi et. al. (2021) has
demonstrated the existence of such waves for two classes of regularisations,
including viscous relaxation. Their analysis uses geometric singular
perturbation theory: for sufficiently small values of a parameter $\varepsilon
> 0$ characterising the `strength' of the regularisation, the waves are
constructed as perturbations of a singular heteroclinic orbit. Here we show
rigorously that these waves are spectrally stable for the case of viscous
relaxation. Our approach is to show that for sufficiently small
$\varepsilon>0$, the `full' eigenvalue problem of the regularised system is
controlled by a (reduced) slow eigenvalue problem defined for $\varepsilon =
0$. In the course of our proof, we examine the ways in which this geometric
construction complements and differs from constructions of other reduced
eigenvalue problems that are known in the wave stability literature.
