We show that the dynamic nonequilibrium segmental concentration profile of a single nanochannel confined DNA molecule can be described via a partial differential evolution equation based on nonlinear diffusion, using an approach analogous to that used in the description of many-molecule systems such as polymer solutions. This equation can describe the segmental concentration profile of a single polymer along the nanochannel as a function of time for chain behavior ranging from states of high compression to equilibrium. In particular, to demonstrate the generality of our approach, we show that our model can describe two distinct types of experimental behavior generated via a sliding bead assay, symmetric relaxation resulting from free expansion of the polymer after compression, and the evolution of DNA concentration "shock waves" as a molecule is driven from equilibrium to a compressed state.