论文标题
在不对称度量空间和应用中梯度流动
Gradient flows in asymmetric metric spaces and applications
论文作者
论文摘要
本文通过离散近似值来研究不对称度量空间中梯度流动的研究（例如，不可逆转的鳍歧管和Minkowski Normed Space）。我们研究了不对称度量空间中曲线和上梯度的基本特性，并确定了最大斜率曲线的存在，该曲线在非平滑环境中被视为梯度曲线。 {介绍}对潜在函数的自然凸度假设，{称为$（p，λ）$ - 凸度，}我们还获得了对最大斜率曲线的渐近行为的一些正则影响。应用包括芬斯勒歧管中梯度流的几个存在结果，{Infinite-Dimensional Funk spaces}上的双线非线性差分进化方程}以及紧凑型Finsler歧管上的热流。
This paper is devoted to the investigation of gradient flows in asymmetric metric spaces (for example, irreversible Finsler manifolds and Minkowski normed spaces) by means of discrete approximation. We study basic properties of curves and upper gradients in asymmetric metric spaces, and establish the existence of a curve of maximal slope, which is regarded as a gradient curve in the non-smooth setting. { Introducing} a natural convexity assumption on the potential function, { which is called the $(p,λ)$-convexity,} we also obtain some regularizing effects on the asymptotic behavior of curves of maximal slope. Applications include several existence results for gradient flows in Finsler manifolds, doubly nonlinear differential evolution equations on { infinite-dimensional Funk spaces}, and heat flow on compact Finsler manifolds.
