Abstract
In this paper, we study the gradient estimates for positive solutions to the following parabolic Lichnerowicz equations ∂u ∂t = � u + hu(x, t )+ Au p (x, t )+ Bu -q (x, t) on complete noncompact Riemannian manifolds, where h, p, q, A, B are real constants and p >1 ,q >0 . MSC: Primary 58J05; secondary 58J35
Highlights
Let M be an n-dimensional complete noncompact Riemannian manifold
We study the gradient estimates for positive solutions to the following parabolic Lichnerowicz equations
We study the following nonlinear parabolic equation ut(x, t) = u(x, t) + hu(x, t) + Aup(x, t) + Bu–q(x, t), ( . )
Summary
Let M be an n-dimensional complete noncompact Riemannian manifold. In this paper, we study the following nonlinear parabolic equation ut(x, t) = u(x, t) + hu(x, t) + Aup(x, t) + Bu–q(x, t), ( . )where h, p, q, A, B are real constants and p > , q > .Gradient estimates play an important role in the study of PDE, especially the Laplace equation and heat equation. We study the gradient estimates for positive solutions to the following parabolic Lichnerowicz equations ∂t on complete noncompact Riemannian manifolds, where h, p, q, A, B are real constants and p > 1, q > 0. Introduction Let M be an n-dimensional complete noncompact Riemannian manifold.
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