Measure-valued solutions to nonlocal transport equations on networks
Analysis of PDEs
2018-04-04 v2
Abstract
We study a nonlinear transport equation defined on an oriented network where the velocity field depends not only on the state variable, but also on the solution itself. We prove existence, uniqueness and continuous dependence results for the solution of the problem intended in a suitable measure-theoretic sense. We also provide a representation formula in terms of the push-forward of the initial and boundary data along the network and discuss an example of nonlocal velocity field fitting our framework.
Cite
@article{arxiv.1709.03930,
title = {Measure-valued solutions to nonlocal transport equations on networks},
author = {Fabio Camilli and Raul De Maio and Andrea Tosin},
journal= {arXiv preprint arXiv:1709.03930},
year = {2018}
}