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math.AP2026
Local analytic well-posedness for one-dimensional Vlasov$\unicode{x2013}$Dirac$\unicode{x2013}$Benney-type equations
Nuno J. Alves, Peter Markowich, Athanasios E. Tzavaras
We study a one-dimensional nonlinear Vlasov equation with a local self-consistent force field generated by the density, where the force is given by the spatial derivative of a real…
math.AP2025
Gradient Flows for the -Laplacian Arising from Biological Network Models: A Novel Dynamical Relaxation Approach
Jan Haskovec, Peter Markowich, Stefano Zampini
We investigate a scalar partial differential equation model for the formation of biological transportation networks. Starting from a discrete graph-based formulation on equilateral…