The strong comparison principle in parabolic problems with the p-Laplacian in a domain

We investigate some strong comparison principles for nonnegative solutions to several parabolic problems with the p-Laplace operator in one space dimension. We focus on the special case of comparing a stationary (i.e., time-independent) solution with a time-dependent solution. We take advantage of some special properties of stationary solutions that, in general, might not hold for time-dependent solutions.