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Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion
Local Global Well-Posedness Aggregation Equations Patlak-Keller-Segel Models Degenerate Diffusion
2010/12/6
Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification...
Intermediate asymptotics for critical and supercritical aggregation equations and Patlak-Keller-Segel models
critical supercritical aggregation equations Patlak-Keller-Segel models
2010/12/15
We examine the long-term asymptotic behavior of dissipating solutions to aggregation equations
and Patlak-Keller-Segel models with degenerate power-law and linear diffusion. The purpose
of this work...
Global Minimizers for Free Energies of Subcritical Aggregation Equations with Degenerate Diffusion
Global Minimizers Free Energies of Subcritical Aggregation Equations Degenerate Diffusion
2010/12/14
We prove the existence of non-trivial global minimizers of a class of free energies related to aggregation equations with degenerate diffusion on Rd. Such equations arise in mathematical biology as mo...