On the well-posedness for Keller-Segel system with fractional diffusion

Communicated by M. Costabel In this paper, we study the Cauchy problem for the Keller–Segel system with fractional diffusion generalizing the Keller–Segel model of chemotaxis for the initial data (u0,v0) in critical Fourier‐Herz spaces B˙q2−2αRn×B˙q2−2αRn with q ∈ [2, ∞], where 1 < α ≤ 2. Making...

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Bibliographic Details
Published in:	Mathematical methods in the applied sciences Vol. 34; no. 14; pp. 1739 - 1750
Main Authors:	Wu, Gang, Zheng, Xiaoxin
Format:	Journal Article
Language:	English
Published:	Chichester, UK John Wiley & Sons, Ltd 30.09.2011 Wiley
Subjects:	Exact sciences and technology fractional diffusion Functional analysis Global analysis, analysis on manifolds Ill-posedness Keller-Segel model Mathematical analysis Mathematics nonlinear evolution equations nonlinear parabolic equations Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Partial differential equations Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Well-posedness Keller-Segel model Numerical linear algebra Fourier analysis Evolution equation Well posed problem Littlewood Paley theory Mathematical method Cauchy problem Non linear equation Regularization method Parabolic equation Numerical analysis fractional diffusion Linear equation III-posedness Applied mathematics nonlinear parabolic equations Ill posed problem Localization nonlinear evolution equations Well-posedness
ISSN:	0170-4214, 1099-1476
Online Access:	Get full text
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