Gradient estimates for a nonlinear parabolic equation with potential under geometric flow

2014/09/03 by Abimbola Abolarinwa, Abolarinwa, Abimbola
Mathematics · #35K55 #53C21 #53C44 #58J35 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1409.0933

openalex publication_date 2014/09/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let (M, g) be an dimensional complete Riemannian manifold. In this paper we prove local Li-Yau type gradient estimates for all positive solutions to the following nonlinear parabolic equation (∂_t - Δ_g + R) u(x, t) = - a u(x, t) log u(x, t) along the generalised geometric flow. Here R = R (x, t) is a smooth potential function and a is a constant. As an application we derived a global estimate and a space-time Harnack inequality.

Citations

• On the parabolic kernel of the Schrödinger operator

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