## 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.

Translated title of the contribution | Gradient flows in asymmetric metric spaces |
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Original language | English |

Pages (from-to) | 5820 - 5834 |

Number of pages | 15 |

Journal | Nonlinear Analysis: Theory, Methods and Applications |

Volume | 71 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1 Dec 2009 |