期刊
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
卷 35, 期 2, 页码 133-168出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-008-0200-7
关键词
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资金
- Spanish-MCI project MTM [2008-06349-C03-03, OT2008]
- ICREA Funding Source: Custom
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 away 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 is an element of (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 is an element of (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.
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