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Updated: Apr 5, 2026

Single-Molecule Diffusion and Assembly on Polymer-Crowded Lipid Membranes
Published on: July 19, 2022
Some free boundary problems involving non-local diffusion and aggregation
José Antonio Carrillo1, Juan Luis Vázquez2
1Department of Mathematics, Imperial College London, London SW7 2AZ, UK juanluis.vazquez@uam.es.
Abstract:
We report on recent progress in the study of evolution processes involving degenerate parabolic equations which may exhibit free boundaries. The equations we have selected follow two recent trends in diffusion theory: considering anomalous diffusion with long-range effects, which leads to fractional operators or other operators involving kernels with large tails; and the combination of diffusion and aggregation effects, leading to delicate long-term equilibria whose description is still incipient.
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