This paper deals with the gradient estimates of the Hamilton type for the positive solutions to the following nonlinear diffusion equation：on a complete noncompact Riemannian manifold with a Bakry-Emery Ricci curvatu...This paper deals with the gradient estimates of the Hamilton type for the positive solutions to the following nonlinear diffusion equation：on a complete noncompact Riemannian manifold with a Bakry-Emery Ricci curvature bounded below by -K （K 〉 0）, where φ is a C2 function, a（x） and b（x） are C1 functions with certain conditions.展开更多
Let M be a noncompact complete Riemannian manifold.In this paper,we consider the following nonlinear parabolic equation on M ut(x,t)=△u(x,t)+au(x,t)ln u(x,t)+bu^α(x,t).We prove a Li–Yau type gradient estimate for p...Let M be a noncompact complete Riemannian manifold.In this paper,we consider the following nonlinear parabolic equation on M ut(x,t)=△u(x,t)+au(x,t)ln u(x,t)+bu^α(x,t).We prove a Li–Yau type gradient estimate for positive solutions to the above equation;as an application,we also derive the corresponding Harnack inequality.These results generalize the corresponding ones proved by Li(J Funct Anal 100:233–256,1991).展开更多
基金supported by the National Natural Science Foundation of China(Nos.11171253,11471175)the Fujian Provincial National Natural Science Foundation of China(No.2012J01015)+1 种基金the Startup Foundation for Introducing Talent of Nuist(No.2014r030)the Pre-research Foundation of NSFC(No.2014x025)
文摘This paper deals with the gradient estimates of the Hamilton type for the positive solutions to the following nonlinear diffusion equation：on a complete noncompact Riemannian manifold with a Bakry-Emery Ricci curvature bounded below by -K （K 〉 0）, where φ is a C2 function, a（x） and b（x） are C1 functions with certain conditions.
基金Supported partially by NSF of China(No.11171253).
文摘Let M be a noncompact complete Riemannian manifold.In this paper,we consider the following nonlinear parabolic equation on M ut(x,t)=△u(x,t)+au(x,t)ln u(x,t)+bu^α(x,t).We prove a Li–Yau type gradient estimate for positive solutions to the above equation;as an application,we also derive the corresponding Harnack inequality.These results generalize the corresponding ones proved by Li(J Funct Anal 100:233–256,1991).
