The total variation flow in metric graphs

Abstract

Our aim is to study the total variation flow in metric graphs. First, we define the functions of bounded variation in metric graphs and their total variation, we also give an integration by parts formula. We prove existence and uniqueness of solutions and that the solutions reach the mean of the initial data in finite time. Moreover, we obtain explicit solutions.

Keywords

• metric graphs
• functions of total variation
• total variation flow
• the -laplacian
• asymptotic behaviour