Gradient flows for bounded linear evolution equations

IF 0.7 3区数学 Q2 MATHEMATICS

Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2021-10-05 DOI:10.4171/zaa/1706

D. M. Renger, Stefanie Schindler

引用次数: 0

Abstract

We study linear evolution equations in separable Hilbert spaces defined by a bounded linear operator. We answer the question which of these equations can be written as a gradient flow, namely those for which the operator is real diagonalisable. The proof is constructive, from which we also derive geodesic lambda-convexity.

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有界线性演化方程的梯度流

研究了由有界线性算子定义的可分离Hilbert空间中的线性演化方程。我们回答了这些方程中哪一个可以写成梯度流的问题，即那些算子是实对角的。这个证明是建设性的，由此我们也得到了测地线的凸性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Zeitschrift fur Analysis und ihre Anwendungen 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications. To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.