References of "Zhu, Xiaorui"
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See detailLi-Yau Harnack Estimates for a Heat-Type Equation Under the Geometric Flow
Li, Yi UL; Zhu, Xiaorui

in Potential Analysis (2018)

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See detailHarnack estimates for a nonlinear parabolic equation under Ricci flow
Li, Yi UL; Zhu, Xiaorui

in Differential Geometry & its Applications (2018), 56

In this paper, we consider the Harnack estimates for a nonlinear parabolic equation under the Ricci flow. The gradient estimates for positive solutions as well as Li-Yau type inequalities are also given.

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See detailHarnack estimates for nonlinear parabolic equations under the Ricci flow
Li, Yi UL; Zhu, Xiaorui

E-print/Working paper (2017)

In this paper, we consider first the Li-Yau Harnack estimates for a nonlinear parabolic equation $\partial_{t}u=\Delta_{t}u-qu -au(\ln u)^{\alpha}$ under the Ricci flow, where $\alpha>0$ is a constant. To ... [more ▼]

In this paper, we consider first the Li-Yau Harnack estimates for a nonlinear parabolic equation $\partial_{t}u=\Delta_{t}u-qu -au(\ln u)^{\alpha}$ under the Ricci flow, where $\alpha>0$ is a constant. To extend these estimates to a more general situation, in the second part, we consider the gradient estimates for a positive solution of the nonlinear parabolic equation $\partial _{t}u=\Delta _{t}u+hu^{p}$ on a Riemannian manifold whose metrics evolve under the geometric flow $\partial _{t}g(t)=-2S_{g(t)}$. To obtain these estimates, we introduce a quantity $\underline{\boldsymbol{S}}$ along the flow which measures whether the tensor $S_{ij}$ satisfies the second contracted Bianchi identity. Under conditions on ${\rm Ric}_{g(t)}, S_{g(t)}$, and $\underline{\boldsymbol{S}}$, we obtain the gradient estimates. [less ▲]

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See detailHarnack estimates for a heat-type equation under the Ricci flow
Li, Yi UL; Zhu, Xiaorui

in Journal of Differential Equations (2016), 260(4), 3270-3301

In this paper, we consider the gradient estimates for a positive solution of the nonlinear parabolic equation ∂tu=Δtu+hup∂tu=Δtu+hup on a Riemannian manifold whose metrics evolve under the Ricci flow. Two ... [more ▼]

In this paper, we consider the gradient estimates for a positive solution of the nonlinear parabolic equation ∂tu=Δtu+hup∂tu=Δtu+hup on a Riemannian manifold whose metrics evolve under the Ricci flow. Two Harnack inequalities and other interesting results are obtained. [less ▲]

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See detailLi-Yau estimates for a nonlinear parabolic equation on manifolds
Li, Yi UL; Zhu, Xiaorui

in Mathematical Physics, Analysis and Geometry (2014)

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