| Abstract: |
| The current paper is concerned with the persistence and spreading speeds of the
following Keller-Segel chemoattraction system in shifting environments,
\begin{equation}\label{abstract-eq1}
\begin{cases}
u_t=u_{xx}-\chi(uv_x)_x +u(r(x-ct)-bu),\quad x\in\R\cr
0=v_{xx}- \nu v+\mu u,\quad x\in\R,
\end{cases}
\end{equation}
where $\chi$, $b$, $\nu$, and $\mu$ are positive constants, { $c\in\R$ }, $r(x)$ is H\older continuous, bounded,
$r^*=\sup_{x\in\R}r(x)>0$, $r(\pm \infty):=\lim_{x\to \pm\infty}r(x)$ exist, and $r(x)$ satisfies either $r(-\infty) |
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