Quantitative stability for quasilinear parabolic equations

We examine the stability of a class of quasilinear parabolic partial differential equations under perturbations. We are interested in the behavior of viscosity solutions as the perturbation parameter vanishes and establish explicit convergence rates by adapting standard comparison arguments. Despite the possible singular or degenerate nature of the parabolic operator, our framework covers, in particular, both the normalized and the variational $p$-parabolic equations, providing quantitative estimates for perturbations of the exponent $p$ and limits arising from regularized approximations.