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math.AP2014★ 93 cited
Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit
Marco Di Francesco, Massimiliano D. Rosini
We prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the…
math.AP2014
Asymptotic Behavior of Gradient Flows Driven by Nonlocal Power Repulsion and Attraction Potentials in One Dimension
Marco Di Francesco, Massimo Fornasier, Jan-Christian Hütter +1
We study the long time behavior of the Wasserstein gradient flow for an energy functional consisting of two components: particles are attracted to a fixed profile by means of a…