半线性热方程的矩阵哈纳克不等式

IF 1.4 4区工程技术 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Mathematics in Engineering Pub Date : 2021-07-29 DOI:10.3934/mine.2023003

G. Ascione, D. Castorina, G. Catino, C. Mantegazza

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引用次数: 1

摘要

我们推导了黎曼流形上具有非负截面曲率和平行里奇张量的半线性热方程正解的Li & you型估计的矩阵版本，类似于R. Hamilton在[5]中对标准热方程所做的。然后我们应用这些估计得到了一些harnack型不等式，这些不等式给出了有关几何量的解的局部边界。

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A matrix Harnack inequality for semilinear heat equations

We derive a matrix version of Li & Yau–type estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative sectional curvatures and parallel Ricci tensor, similarly to what R. Hamilton did in ^[5] for the standard heat equation. We then apply these estimates to obtain some Harnack–type inequalities, which give local bounds on the solutions in terms of the geometric quantities involved.

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