On Patlak-Keller-Segel system for several populations: A gradient flow approach
نویسندگان
چکیده
منابع مشابه
On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
This review is dedicated to recent results on the 2d parabolic-elliptic PatlakKeller-Segel model, and on its variant in higher dimensions where the diffusion is of critical porous medium type. Both of these models have a critical mass Mc such that the solutions exist globally in time if the mass is less than Mc and above which there are solutions which blowup in finite time. The main tools, in ...
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A finite volume method is presented to discretize the Patlak-Keller-Segel (PKS) model for chemosensitive movements. On the one hand, we prove existence and uniqueness of a numerical solution to the proposed scheme. On the other hand, we give a priori estimates and establish a threshold on the initial mass, for which we show that the numerical approximation convergences to the solution to the PK...
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This paper is devoted to the analysis of non-negative solutions for a generalisation of the classical parabolic-elliptic PatlakKeller-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...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2019
ISSN: 0022-0396
DOI: 10.1016/j.jde.2019.08.004