On equations of continuity and transport type on metric graphs and
fractals
On equations of continuity and transport type on metric graphs and
fractals
We study first order equations of continuity and transport type on metric spaces of martingale dimension one, including finite metric graphs, p.c.f. self-similar sets and classical Sierpi\'nski carpets. On such spaces solutions of the continuity equation in the weak sense are generally non-unique. We use semigroup theory to prove a …