Ricci- Yamabe 流下一类非线性抛物型方程正解的梯度估计及其应用
Gradient Estimates of PositiveSolutions for a General of NonlinearParabolic Equations under theRicci-Yamabe Flow and Its Applications
DOI: 10.12677/PM.2025.1511267, PDF,   
作者: 康彩霞：西北师范大学数学与统计学院，甘肃兰州
关键词: 梯度估计；Harnack不等式；Ricci-Yamabe流；Gradient Estimates； Harnack Inequality； Ricci-Yamabe Flow
摘要: 本文讨论了黎曼流形(Mn, g(x,t))上一类非线性抛物型方程
Abstract: (Δ-∂t)u(x,t)=p(x,t)u(x,t)+q(x,t)ua+1(x,t)正解沿Ricci-Yamabe流演化的情形.其中 p(x,t)，q(x,t)∈ C2,1(Mn×[0,T]), a是任意常数.运用Laplacian比较定理和极大值原理建立两种不同类型的梯度估计(Li-Yau型, Hamilton型),并给出相关应用。In this paper, we prove gradient estimates for positive solutions of a class of nonlinear parabolic equation (Δ-∂t)u(x,t)=p(x,t)u(x,t)+q(x,t)ua+1(x,t)on the Riemannian manifold (Mn, g(x,t)) under the Ricci-Yamabe ow. Here p(x,t)，q(x,t)∈ C2,1(Mn×[0,T]) and a is an arbitrary constant. By using the Laplacian com- parison theorem and the maximum principle, two different types of gradient estimates (Li-Yau type, Hamilton type) are established, and relevant applications are given.
文章引用：康彩霞. Ricci- Yamabe 流下一类非线性抛物型方程正解的梯度估计及其应用[J]. 理论数学, 2025, 15(11): 32-52. https://doi.org/10.12677/PM.2025.1511267

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