Speaker
Description
In this talk we study a dynamic optimal transport type problem on a compact set (bulk) coupled with a non-intersecting and sufficiently regular curve. On each of them, a Benamou-Brenier type dynamic optimal transport problem is considered, yet with an additional mechanism that allows the exchange (at a cost) of mass between bulk and curve. In the respective actions, we allow for non-linear mobilities. Our first result is a proof of existence of minimizers based on the direct method of calculus of variations.
The main interest lies in the case when the curve is also allowed to change. Then, a Tangent-Point energy is added to the action functional in order to preserve the regularity properties of the curve. Also in this case, existence of optimizers is shown.
We extend these analytical findings by numerical simulations based on a primal-dual approach that illustrate the behaviour of geodesics, for fixed and varying curves.
