Paper derives gradient estimates for porous medium equations on Riemannian manifolds.
problem Gradient estimates for porous medium equations on Riemannian manifolds.
method Employing cutoff functions and the maximum principle.
result Derives Hamilton-Souplet-Zhang type gradient estimates for porous medium type equations.
The purpose of this paper is to study gradient estimate of Hamilton - Souplet - Zhang type for the general heat equation ut=ΔVu+aulogu+bu on noncompact Riemannian manifolds. As its application, we show a Harnak inequality for the heat solution and a Liouville type theorem for a nonlinear elliptic equation.…
The article derives gradient estimations for semilinear equations on geometric flows.
problem Gradient estimation for semilinear equations on geometric flows.
method Derives both Hamilton and Souplet-Zhang type gradient estimations.
result Gradient estimations for semilinear equations on geometric flows.
In this paper, we consider gradient estimates for two type of nonlinear parabolic equations under the Ricci flow: one is the equation ut=Δu+aulogu+bu with a,b two real constants, the other is ut=Δu+λuα with λ,α two real constants. By a suitable scaling for the above two equations, we obtain Hamilton-So…
The paper establishes gradient estimates for harmonic and heat equation solutions on manifolds with boundary.
problem Gradient estimates for harmonic and heat equation solutions on manifolds with boundary.
method Yau and Souplet-Zhang type gradient estimates for harmonic and heat equation solutions under Dirichlet boundary condition.
result Established gradient estimates for harmonic and heat equation solutions on manifolds with boundary.
Study gradient estimates for nonlinear parabolic equations on Riemannian manifolds.
problem Estimating gradients for nonlinear parabolic equations on Riemannian manifolds.
method Analyzes Fisher-KPP, parabolic Allen-Cahn, and Newell-Whitehead equations on complete noncompact Riemannian manifolds.
result Gradient estimates for positive solutions and Liouville theorem for ancient solutions.
The paper provides gradient estimates for specific evolution equations on metric measure spaces.
problem Gradient estimates for a class of evolution equations on smooth metric measure spaces.
method Local gradient estimates of Souplet-Zhang type and gradient estimates of Hamilton type.
result Gradient estimates for positive solutions of the evolution equation on smooth metric measure spaces.
The paper derives gradient estimates for porous medium and fast diffusion equations on metric measure spaces.
problem Gradient estimates for porous medium and fast diffusion equations on metric measure spaces.
method Derives Li-Yau and Souplet-Zhang type gradient estimates for the given equations.
result Gradient estimates for the equations on complete noncompact metric measure spaces with compact boundary.
In this paper, we study elliptic gradient estimates for a nonlinear f-heat equation, which is related to the gradient Ricci soliton and the weighted log-Sobolev constant of smooth metric measure spaces. Precisely, we obtain Hamilton's and Souplet-Zhang's gradient estimates for positive solutions to the nonlinear f-…
The paper proves gradient estimates for nonlinear parabolic equations on smooth metric measure spaces.
problem Proving gradient estimates for nonlinear parabolic equations on smooth metric measure spaces.
method Using Souplet-Zhang type estimates and properties of Bakry-Emery Ricci tensor and weighted mean curvature.
result Gradient estimates for nonlinear parabolic equations on smooth metric measure spaces with Dirichlet boundary condition.
Sharp gradient estimates for heat equation in Riemannian manifolds proved.
problem Proving sharp gradient estimates for heat equation in Riemannian manifolds.
method Analyzing the heat equation ut=Δu+aulogu in complete noncompact Riemannian manifolds. result Gradient estimates are sharp and imply that if u is a positive solution of ut=Δu and logu is of sublinear growth, then u must be constant.