AI Article Synopsis
- The study focuses on the evolution processes related to degenerate parabolic equations, highlighting their potential to have free boundaries.
- It addresses two current trends in diffusion theory: the exploration of anomalous diffusion with long-range effects and the use of fractional operators.
- The research also investigates how diffusion and aggregation effects can lead to complex long-term equilibria that are still not fully understood.
Article 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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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4535263 | PMC |
| http://dx.doi.org/10.1098/rsta.2014.0275 | DOI Listing |
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