Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
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2009Permanent link to this record
http://hdl.handle.net/10754/671195
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This paper is devoted to the analysis of non-negative solutions for a generalisation of the classical parabolic-elliptic Patlak-Keller-Segel system with d 3 and porous medium-like non-linear diffusion. Here, the non-linear diffusion is chosen in such a way that its scaling and the one of the Poisson term coincide. We exhibit that the qualitative behaviour of solutions is decided by the initial mass of the system. Actually, there is a sharp critical mass M c such that if M in (0, M-c] solutions exist globally in time, whereas there are blowing-up solutions otherwise. We also show the existence of self-similar solutions for M in (0, M-c). While characterising the possible infinite time blowing-up profile for M = M c , we observe that the long time asymptotics are much more complicated than in the classical Patlak-Keller-Segel system in dimension two. © 2008 Springer-Verlag.Citation
Blanchet, A., Carrillo, J. A., & Laurençot, P. (2008). Critical mass for a Patlak–Keller–Segel model with degenerate diffusion in higher dimensions. Calculus of Variations and Partial Differential Equations, 35(2), 133–168. doi:10.1007/s00526-008-0200-7Sponsors
KAUST investigator award.Publisher
Springer Science and Business Media LLCarXiv
0801.2310Additional Links
http://link.springer.com/10.1007/s00526-008-0200-7ae974a485f413a2113503eed53cd6c53
10.1007/s00526-008-0200-7