论文标题
概率度量空间中梯度流的不变性原理
An invariance principle for gradient flows in the space of probability measures
论文作者
论文摘要
我们试图为梯度流以最佳运输距离描述的一般进化PDE建立定性收敛结果。这些定性融合结果来自Lasalle不变性原理的一般名称的动力系统。通过结合梯度流理论和动力学系统的一些基本概念，我们能够在一般假设下的进化PDE中重现这种不变性原理。我们将此抽象理论应用于恢复，简化甚至扩展其各自文献中结果的示例的非竭尽全力列表。
We seek to establish qualitative convergence results to a general class of evolution PDEs described by gradient flows in optimal transportation distances. These qualitative convergence results come from dynamical systems under the general name of LaSalle Invariance Principle. By combining some of the basic notions of gradient flow theory and dynamical systems, we are able to reproduce this invariance principle in the setting of evolution PDEs under general assumptions. We apply this abstract theory to a non-exhaustive list of examples that recover, simplify, and even extend the results in their respective literatures.
