Local Hamilton type Gradient Estimates and Harnack Inequalities for Nonlinear Parabolic Equations on Riemannian Manifolds

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2024年3月27日

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Wen Wang,
Da-peng Xie,
Hui Zhou

摘要

In this paper, we prove a local Hamilton type gradient estimate for positive solution of the nonlinear parabolic equation \({u_t}(x,t) = \Delta u(x,t) + au(x,t)\ln \,u(x,t) + b{u^\alpha }(x,t),\) on M × (−∞, ∞) with α ∈ R, where a and b are constants. As application, the Harnack inequalities are derived.