Memory effects in measure transport equations
Analysis of PDEs
2019-04-16 v2
Abstract
Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the time-derivative with power-law kernels, are typical for memory effects in complex systems. In this paper we consider a nonlinear transport equation with a fractional time-derivative. We provide a well-posedness theory for weak measure solutions of the problem and an integral formula which generalizes the classical push-forward representation formula to this setting.
Cite
@article{arxiv.1806.10331,
title = {Memory effects in measure transport equations},
author = {Fabio Camilli and Raul De Maio},
journal= {arXiv preprint arXiv:1806.10331},
year = {2019}
}