Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-time blow-up prevention by logistic source in parabolic-elliptic
  chemotaxis models with singular sensitivity in any dimensional setting   In recent years, it has been drawn a lot of attention to the question of
whether logistic kinetics is sufficient to enforce the global existence of
classical solutions or to prevent finite-time blow-up in various chemotaxis
models. However, for several important chemotaxis models, only in the space two
dimensional setting, it has been shown that logistic kinetics is sufficient to
enforce the global existence of classical solutions (see [15] and [34]). The
current paper is to give a confirmed answer to the above question for the
following parabolic-elliptic chemotaxis system with singular sensitivity and
logistic source in any space dimensional setting, \begin{equation}
\begin{cases} u_t=\Delta u-\chi\nabla\cdot (\frac{u}{v} \nabla
v)+u(a(x,t)-b(x,t) u),\quad x\in \Omega\cr 0=\Delta v-\mu v+\nu u,\quad x\in
\Omega \quad \cr \frac{\partial u}{\partial n}=\frac{\partial v}{\partial
n}=0,\quad x\in\partial\Omega, \end{cases} \end{equation} where $\Omega \subset
\mathbb{R}^n$ is a bounded domain with smooth boundary $\partial\Omega$, $\chi$
is the singular chemotaxis sensitivity coefficient, $a(x,t)$ and $b(x,t)$ are
positive smooth functions, and $\mu,\nu$ are positive constants. We prove that,
for any given nonnegative initial data $0\not\equiv u_0\in C^0(\bar \Omega)$,
(0.1) has a unique globally defined classical solution
$(u(t,x;u_0),v(t,x;u_0))$ with $u(0,x;u_0)=u_0(x)$, which shows that, in any
space dimensional setting, logistic kinetics is sufficient to enforce the
global existence of classical solutions and hence prevents the occurrence of
finite-time blow-up even for arbitrarily large $\chi$. In addition, the
solutions are shown to be uniformly bounded under the conditions
$a_{\inf}>\frac{\mu \chi^2}{4}$ when $\chi \leq 2$ and $a_{\inf}>\mu (\chi-1)$
when $\chi>2$.

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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th