Some free boundary problems involving non-local diffusion and aggregation.
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.
Department of Mathematics, Imperial College London, London SW7 2AZ, UK juanluis.vazquez@uam.es.
José Antonio
JA
Carrillo
Departmento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain.
Juan Luis
JL
Vázquez
aggregation; interaction energy; non-local diffusion; obstacle problems