Uniform in time interacting particle approximations for nonlinear equations of Patlak-Keller-Segel type
نویسندگان
چکیده
منابع مشابه
Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion
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 and generalization of the well-posedness theory of these models. We prove local well-posedness on bounded domains for dimensions d ≥ 2 and in all of space for d ≥ 3, the uniqueness being a result ...
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The L-critical parabolic-elliptic Patlak-Keller-Segel system is a classical model of chemotactic aggregation in micro-organisms well-known to have critical mass phenomena [10, 8]. In this paper we study this critical mass phenomenon in the context of Patlak-Keller-Segel models with spatially varying diffusivity and decay rate of the chemo-attractant. The primary tool for the proof of global exi...
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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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In this paper we study the controllability of the Keller-Segel system approximating its parabolic-elliptic version. We show that this parabolic system is locally uniform controllable around a constant solution of the parabolic-elliptic system when the control is acting on the component of the chemical. Résumé. Dans cet article, nous étudions la contrôlabilité du système de Keller-Segel qui appr...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2017
ISSN: 1083-6489
DOI: 10.1214/17-ejp25