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The Royal Society, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2050(373), p. 20140275, 2015

DOI: 10.1098/rsta.2014.0275

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Some free boundary problems involving non-local diffusion and aggregation

Journal article published in 2015 by Jose Antonio Carrillo ORCID, Juan Luis Vazquez
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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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.