Gradient estimates for a weighted parabolic equation under geometric\n flow

2021/11/30 by Shahroud Azami, Azami, Shahroud
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2112.01271

Abstract

Let (Mⁿ,g,e^-\φdv) be a weighted Riemannian manifold evolving by\ngeometric flow \(\∂ g)/(\∂ t)=2h(t), , , ,\(\∂\n\φ)/(\∂ t)=\Δ \φ. In this paper, we obtain a series of space-time\ngradient estimates for positive solutions of a parabolic partial equation\n(
Delta
_phi-
partial_t)u(x,t)=q(x,t)u^a+1(x,t)+p(x,t)A(u(x,t))),
,
,
,
,(x,t)
in\nM
times[0,T] on a weighted Riemannian manifold under geometric flow. By\nintegrating the gradient estimates, we find the corresponding Harnack\ninequalities.\n

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