Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities

We study a quasilinear parabolic equation of forward-backward type, under assumptions on the nonlinearity which hold for a wide class of mathematical models, using a pseudo-parabolic regularization of power type. We prove existence and uniqueness of positive solutions of the regularized problem in a space of Radon measures. It is shown that these solutions satisfy suitable entropy inequalities. We also study their qualitative properties, in particular proving that the singular part of the solution with respect to the Lebesgue measure is constant in time.