Gradient Estimates for a Nonlinear Heat Equation Under Finsler-geometric Flow

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Gradient estimate nonlinear heat equation Harnack inequality Akbarzadeh's Ricci tensor Finsler-geometric flow
• 年，卷（期）: 2020,（1）
• 页码范围: 17-38
• 页数: 22页
• 分类号: O175.26
• 语种: 英文
• DOI: 10.4208/jpde.v33.n1.2

摘要

This paper considers a compact Finsler manifold (Mn,F(t),m) evolving under a Finsler-geometric flow and establishes global gradient estimates for positive solutions of the following nonlinear heat equation (a)tu(x,t)=△mu(x,t),(x,t)∈M×[0,T],where △m is the Finsler-Laplacian.By integrating the gradient estimates,we derive the corresponding Harnack inequalities.Our results generalize and correct the work of S.Lakzian,who established similar results for the Finsler-Ricci flow.Our results are also natural extension of similar results on Riemannian-geometric flow,previously studied by J.Sun.Finally,we give an application to the Finsler-Yamabe flow.