40 citations · 65 across the 4 of their papers we have counts for
4 papers · 1 filter
On a Class of Nonlocal Continuity Equations on Graphs
A. Esposito, F. S. Patacchini, A. Schlichting
Motivated by applications in data science, we study partial differential equations on graphs. By a classical fixed-point argument, we show existence and uniqueness of solutions to…
Well-posedness and asymptotic behaviour of an aggregation model with intrinsic interactions on sphere and other manifolds
Razvan C. Fetecau, Hansol Park, Francesco S. Patacchini
We investigate a model for collective behaviour with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure solutions (defined via mass transpor…
Convergence of a particle method for diffusive gradient flows in one dimension
J. A. Carrillo, F. S. Patacchini, P. Sternberg +1
We prove the convergence of a particle method for the approximation of diffusive gradient flows in one dimension. This method relies on the discretisation of the energy via non-ove…
Numerical Study of a Particle Method for Gradient Flows
J. A. Carrillo, Y. Huang, F. S. Patacchini +1
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-ov…