3 papers
math.AP2018
A Hopf-Lax formula for Hamilton-Jacobi equations with Caputo time derivative
Fabio Camilli, Raul De Maio, Elisa Iacomini
We prove a representation formula of Hopf-Lax type for the solution of a Hamilton-Jacobi equation involving Caputo time-fractional derivative. Equations of these type are associate…
math.AP2017
Measure-valued solutions to nonlocal transport equations on networks
Fabio Camilli, Raul De Maio, Andrea Tosin
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 ex…
math.AP2016
Transport of measures on networks
Fabio Camilli, Raul De Maio, Andrea Tosin
In this paper we formulate a theory of measure-valued linear transport equations on networks. The building block of our approach is the initial/boundary-value problem for the measu…