切向热方程的几何起源和一些性质

IF 0.8 Q2 MATHEMATICS Tunisian Journal of Mathematics Pub Date : 2019-01-01 DOI:10.2140/TUNIS.2019.1.561
Y. Brenier
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引用次数: 3

摘要

通过适当的二次时间变化,从闵可夫斯基时空的最小曲面方程出发,推导出与平均曲率流动方程对偶的,具有arcarcential非线性的非线性热方程∂t D =∆(arctan D)的几何原点。在考察了切向热方程的各种性质(特别是通过其最优输运解释和它与波恩-因菲尔德电磁学理论的关系)之后,我们将简要讨论它在图像处理中的可能用途,一旦以非保守形式书写并适当离散。
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Geometric origin and some properties of the arctangential heat equation
We establish the geometric origin ot the nonlinear heat equation with arct-angential nonlinearity: ∂ t D = ∆(arctan D) by deriving it, together and in du-ality with the mean curvature flow equation, from the minimal surface equation in Minkowski space-time, through a suitable quadratic change of time. After examining various properties of the arctangential heat equation (in particular through its optimal transport interpretation a la Otto and its relationship with the Born-Infeld theory of Electromagnetism), we shortly discuss its possible use for image processing, once written in non-conservative form and properly discretized.
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来源期刊
Tunisian Journal of Mathematics
Tunisian Journal of Mathematics Mathematics-Mathematics (all)
CiteScore
1.70
自引率
0.00%
发文量
12
期刊最新文献
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