7 papers
Numerical validation of an adaptive model for the determination of nonlinear-flow regions in highly heterogeneous porous media
Alessio Fumagalli, Francesco S. Patacchini
An adaptive model for the description of flows in highly heterogeneous porous media is developed in~\cite{FP21,FP23}. There, depending on the magnitude of the fluid's velocity, the…
Well-posedness of an interaction model on Riemannian manifolds
Razvan C. Fetecau, Francesco S. Patacchini
We investigate a model for collective behaviour with intrinsic interactions on smooth Riemannian manifolds. For regular interaction potentials, we establish the local well-posednes…
The nonlocal-interaction equation near attracting manifolds
Francesco S. Patacchini, Dejan Slepčev
We study the approximation of the nonlocal-interaction equation restricted to a compact manifold embedded in , and more generally compact sets with posi…
Model adaptation in a discrete fracture network: existence of solutions and numerical strategies
Alessio Fumagalli, Francesco Saverio Patacchini
Fractures are normally present in the underground and are, for some physical processes, of paramount importance. Their accurate description is fundamental to obtain reliable numeri…
Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit
Antonio Esposito, Francesco S. Patacchini, André Schlichting +1
We consider dynamics driven by interaction energies on graphs. We introduce graph analogues of the continuum nonlocal-interaction equation and interpret them as gradient flows with…
Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour
Mikaela Iacobelli, Francesco Patacchini, Filippo Santambrogio
In this paper we devote our attention to a class of weighted ultrafast diffusion equations arising from the problem of quantisation for probability measures. These equations have a…