TY - JOUR
T1 - Gradient flows in asymmetric metric spaces
AU - Chenchiah, Isaac Vikram
AU - Rieger, Marc Oliver
AU - Zimmer, Johannes
PY - 2009/12/1
Y1 - 2009/12/1
N2 - 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.
AB - 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.
KW - Gradient flow
KW - Quasimetric
UR - http://www.scopus.com/inward/record.url?scp=68349084635&partnerID=8YFLogxK
U2 - 10.1016/j.na.2009.05.006
DO - 10.1016/j.na.2009.05.006
M3 - Article
AN - SCOPUS:68349084635
SN - 0362-546X
VL - 71
SP - 5820
EP - 5834
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 11
ER -