Some free boundary problems involving non-local diffusion and aggregation

被引：14
作者：
Carrillo, Jose Antonio [1 ]
Luis Vazquez, Juan [2 ]
机构：
[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England
[2] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain
来源：
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2015年 / 373卷 / 2050期
基金：
英国工程与自然科学研究理事会;
关键词：
non-local diffusion; interaction energy; aggregation; obstacle problems; POROUS-MEDIUM EQUATIONS; ASYMPTOTIC-BEHAVIOR; OBSTACLE PROBLEM; BARENBLATT PROFILES; NONLINEAR DIFFUSION; STABILITY; REGULARITY; EVOLUTION; DYNAMICS; FINITE;
D O I：
10.1098/rsta.2014.0275
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
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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页数：16
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