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Gradient flows in asymmetric metric spaces


Chenchiah, Isaac Vikram; Rieger, Marc Oliver; Zimmer, Johannes (2009). Gradient flows in asymmetric metric spaces. Nonlinear Analysis: Theory, Methods & Applications, 71(11):5820-5834.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Language:English
Date:1 December 2009
Deposited On:26 Feb 2010 15:40
Last Modified:07 Apr 2017 15:50
Publisher:Elsevier
ISSN:0362-546X
Publisher DOI:https://doi.org/10.1016/j.na.2009.05.006

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