The paper starts with a short review on the history of PDEs and their related inequalities. We present a unified approach to the basic parabolic differential inequalities. It starts in Section 2 with the famous Lemma of Nagumo and leads to recent and new result on parabolic equations with singular nonlinear elliptic operators (7) that include the p-Laplacian and the operator of capillary surfaces. Sections 3 and 4 deal with the one-dimensional case and radial solutions. A Semi-Strong Minimum Principle is found in Section 6.