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.
|Translated title of the contribution||Gradient flows in asymmetric metric spaces|
|Pages (from-to)||5820 - 5834|
|Number of pages||15|
|Journal||Nonlinear Analysis: Theory, Methods and Applications|
|Publication status||Published - 1 Dec 2009|