Gradient flows in asymmetric metric spaces

Isaac Vikram Chenchiah, Marc Oliver Rieger, Johannes Zimmer

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

This article is concerned with gradient flows in asymmetric metric spaces, that is, spaces with a topology induced by an asymmetric metric. Such an asymmetry appears naturally in many applications, e.g., in mathematical models for materials with hysteresis. A framework of asymmetric gradient flows is established under the assumption that the metric is weakly lower-semicontinuous in the second argument (and not necessarily on the first), and an existence theorem for gradient flows defined on an asymmetric metric space is given.

Original languageEnglish
Pages (from-to)5820-5834
Number of pages15
JournalNonlinear Analysis, Theory, Methods and Applications
Volume71
Issue number11
DOIs
StatePublished - 1 Dec 2009
Externally publishedYes

Keywords

  • Gradient flow
  • Quasimetric

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