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Evolution equations on co-evolving graphs: long-time behaviour and the graph continuity equation
José Antonio Carrillo, Antonio Esposito, László Mikolás
We focus on evolution equations on co-evolving, infinite, graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the gra…
Nonlocal particle approximation for linear and fast diffusion equations
José Antonio Carrillo, Antonio Esposito, Jakub Skrzeczkowski +1
We construct deterministic particle solutions for linear and fast diffusion equations using a nonlocal approximation. We exploit the -Wasserstein gradient flow structure of the…
Competing effects in fourth-order aggregation-diffusion equations
José Antonio Carrillo, Antonio Esposito, Carles Falcó +1
We give sharp conditions for global in time existence of gradient flow solutions to a Cahn-Hilliard-type equation, with backwards second order degenerate diffusion, in any dimensio…