黎曼曲面上非线性抛物方程的局部汉密尔顿型梯度估计和哈纳克不等式

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-03-27 DOI:10.1007/s10255-024-1041-7

Wen Wang, Da-peng Xie, Hui Zhou

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引用次数: 0

摘要

本文证明了非线性抛物方程 $${u_t}(x,t) = \Delta u(x,t) + au(x,t)\ln \,u(x,t) + b{u^\alpha }(x,t), $$ 在 M × (-∞, ∞) 上的正解的局部哈密顿梯度估计，α∈ R，其中 a 和 b 是常数。作为应用，得出哈纳克不等式。

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Local Hamilton type Gradient Estimates and Harnack Inequalities for Nonlinear Parabolic Equations on Riemannian Manifolds

In this paper, we prove a local Hamilton type gradient estimate for positive solution of the nonlinear parabolic equation

$${u_t}(x,t) = \Delta u(x,t) + au(x,t)\ln \,u(x,t) + b{u^\alpha }(x,t),$$

on M × (−∞, ∞) with α ∈ R, where a and b are constants. As application, the Harnack inequalities are derived.

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来源期刊

Acta Mathematicae Applicatae Sinica, English Series 数学-应用数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.