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• W2023212073 startingPage "1119" @default.
• W2023212073 abstract "We consider a class of L 1 critical nonlocal aggregation equations with linear or nonlinear porous media-type diffusion which are characterized by a long-range interaction potential that decays faster than the Newtonian potential at infinity. The fast decay breaks the L 1 scaling symmetry and we prove that all ‘sufficiently spread out’ initial data, even with supercritical mass, results in global, decaying solutions. In particular, we produce decaying solutions with arbitrary mass in cases for which finite time blow up solutions or non-decaying solutions are also known to exist for sufficiently large mass. This is in contrast to the classical parabolic-elliptic PKS for which essentially all solutions with supercritical mass blow up in finite time. The results with linear diffusion are proved using properties of the Fokker-Planck semi-group whereas the results with nonlinear diffusion are proved using a more interesting bootstrap argument coupling the entropy-entropy dissipation methods of the porous media equation together with higher L p estimates similar to those used in small-data and local theory for PKS-type equations." @default.
• W2023212073 created "2016-06-24" @default.
• W2023212073 creator A5081815930 @default.
• W2023212073 date "2015-01-20" @default.
• W2023212073 modified "2023-09-25" @default.
• W2023212073 title "Large Mass Global Solutions for a Class of<i>L</i>¹-Critical Nonlocal Aggregation Equations and Parabolic-Elliptic Patlak-Keller-Segel Models" @default.
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• W2023212073 doi "https://doi.org/10.1080/03605302.2014.999938" @default.
• W2023212073 hasPublicationYear "2015" @default.
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