Branching time estimates in quasi-static evolution for the average distance functional
Xiuqing Lu · 2011
We analyze in this paper the discrete quasi-static irreversible with small steps evolution of a connected network related to an average distance functional minimization problem. Our main goal is to determine whether new branches may appear during the evolution, thus changing the topology. We would give conditions on this, and an upper bound for the time at which it must happen for a particular class of configurations. We will use extensively tools belonging to minimizing movements and optimal transportation theory with free Dirichlet regions. Then we will give some explicit examples of quasi-static evolution, whose branching time will be estimated direct computation, by using both pure energy and mixed geometric/energy estimates.