文献类型：期刊文献

英文题名：Gradient flows in asymmetric metric spaces and applications

作者：Ohta, Shin-ichi[1,2];Zhao, Wei[3]

机构：[1]Osaka Univ, Dept Math, Osaka 5600043, Japan;[2]RIKEN Ctr Adv Intelligence Project AIP, 1-4-1 Nihonbashi, Tokyo 1030027, Japan;[3]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2025

卷号：26

期号：2

起止页码：919

外文期刊名：ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001546357700010)】；

基金：The first author was supported by JSPS Grant-in-Aid for Scientific Research (KAKENHI) 22H04942, 19H01786. The second author was supported by Natural Science Foundation of China (No. 12471045) , Natural Science Foundation of Shanghai (Nos. 21ZR1418300, 19ZR1411700) , Ningbo Natural Science Foundation (No. 2024J017) and Science and Technology Project of Xinjiang Production and Construction Corps (No. 2023CB008-12) .

语种：英文

摘要：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, lambda)-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 flows on compact Finsler manifolds.