Abstract
In this paper, we derive several differential Harnack estimates (also known as Li–Yau–Hamilton type estimates) for nonnegative solutions and positive solutions of the porous medium equation ft=ffxx+fx2+f2, which is a nonlinear parabolic equation. Our derivations rely on an idea related to the parabolic maximum principle. We prove these estimates by different methods. As the applications of the estimates, Harnack inequalities are also obtained.
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