parabolicequationtypeharnackdifferentialinequalitylocalhamiltontypegradientestimatefastdiffusionporousmediaequation
摘要：In this paper, let （Mn, g） be an n-dimensional complete Riemannian manifold with the m-dimensional Bakry-Emery Ricci curvature bounded below. By using the maximum principle, we firstprove a Li Yau type Harnack differential inequality for positive solutions to the parabolic equation on compact Riemannian manifolds Mn, where F E ∈2（0, ∞）, F＇ 〉 0 and f is a C^2-smooth functiondefined on M^n. As application, the Harnack differential inequalities for fast diffusion type equationand porous media type equation are derived. On the other hand, we derive a local Hamilton typegradient estimate for positive solutions of the degenerate parabolic equation on complete Riemannianmanifolds. As application, related local Hamilton type gradient estimate and Harnack inequality forfast dfiffusion type equation are established. Our results generalize some known results.
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