Quantum mechanics

Inequality

Laplace operator

Differential equation

Applied mathematics

Operating system

Computer science

Dentistry

Section (typography)

Elliptic partial differential equation

Physics

Nonlinear system

Calculus (dental)

Mathematics

Mathematical analysis

Medicine

Partial differential equation

Parabolic partial differential equation

Discrete and Continuous Dynamical Systems

The paper starts with a short review on the history of PDEs andtheir related inequalities. We present a unified approach to the basic parabolicdifferential inequalities. It starts in Section 2 with the famous Lemmaof Nagumo and leads to recent and new result on parabolic equations withsingular nonlinear elliptic operators (7) that include the p-Laplacian and theoperator of capillary surfaces. Sections 3 and 4 deal with the one-dimensionalcase and radial solutions. A Semi-Strong Minimum Principle is found in Section6.

Nonlinear parabolic differential equations and inequalities