标题： 梯度系统的分析简介 显示英文标题

标题： An introduction to the analysis of gradients systems

摘要： 这些讲义提供了在2022/23年冬季学期于柏林洪堡大学举办的一个小型课程的扩展版本（共计36小时）。 从第5.4节开始添加的材料是后来补充进去的。 这些讲义的目标是概述Hilbert空间、Banach空间和度量空间中梯度流方程的分析方法，并展示这些理论在入门层次上有许多共同之处。 通过适当的例子和反例来说明这些理论及其特定设定。 显示英文摘要

摘要： The present notes provide an extended version of a small lecture course given at the Humboldt Universit\"at zu Berlin in the Winter Term 2022/23 (of 36 hours). The material starting in Section 5.4 was added afterwards. The aim of these notes to give an introductory overview on the analytical approaches for gradient-flow equations in Hilbert spaces, Banach spaces, and metric spaces and to show that on the first entry level these theories have a lot in common. The theories and their specific setups are illustrated by suitable examples and counterexamples.