Affiliation:
1. College of Mathematics Science Chongqing Normal University Chongqing 401331 China
Abstract
In this paper, the local well‐posedness (which means that the initial‐to‐solution map
is existence, uniqueness and continuous) for the Cauchy problem of the Keller‐Segel model with nonlinear chemotactic sensitivity and signal secretion in Besov spaces
with
and
was established, and the solution of PEKS (Keller‐Segel system with
) converges to the solution of HEKS (Keller‐Segel system with
) as the diffusion coefficient
in these Besov spaces was proved. In addition, we show that the solution of this parabolic‐elliptic chemotaxis‐growth system is local well‐posedness in the critical spaces
but ill‐posed (not continuous) in Besov spaces
. Moreover, we show a further continuity result that the initial‐to‐solution map
is Hölder continuous in Besov spaces
equipped with weaker topology. Finally, a blow‐up criteria for the solutions of this system in Besov spaces
was also obtained.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Chongqing
Subject
General Engineering,General Mathematics
Cited by
2 articles.
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