Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global stabilization of the full attraction-repulsion Keller-Segel
  system   We are concerned with the following full Attraction-Repulsion Keller-Segel
(ARKS) system \begin{equation}\label{ARKS}\tag{$\ast$} \begin{cases} u_t=\Delta
u-\nabla\cdot(\chi u\nabla v)+\nabla\cdot(\xi u\nabla w), &x\in \Omega, ~~t>0,
  v_t=D_1\Delta v+\alpha u-\beta v,& x\in \Omega, ~~t>0,
  w_t=D_2\Delta w+\gamma u-\delta w, &x\in \Omega, ~~t>0,\\
u(x,0)=u_0(x),~v(x,0)= v_0(x), w(x,0)= w_0(x) & x\in \Omega, \end{cases}
\end{equation} in a bounded domain $\Omega\subset \R^2$ with smooth boundary
subject to homogeneous Neumann boundary conditions. %The parameters
$D_1,D_2,\chi,\xi,\alpha,\beta,\gamma$ and $\delta$ are positive. By
constructing an appropriate Lyapunov functions, we establish the boundedness
and asymptotical behavior of solutions to the system \eqref{ARKS} with large
initial data. Precisely, we show that if the parameters satisfy
$\frac{\xi\gamma}{\chi\alpha}\geq
\max\Big\{\frac{D_1}{D_2},\frac{D_2}{D_1},\frac{\beta}{\delta},\frac{\delta}{\beta}\Big\}$
for all positive parameters $D_1,D_2,\chi,\xi,\alpha,\beta,\gamma$ and
$\delta$, the system \eqref{ARKS} has a unique global classical solution
$(u,v,w)$, which converges to the constant steady state
$(\bar{u}_0,\frac{\alpha}{\beta}\bar{u}_0,\frac{\gamma}{\delta}\bar{u}_0)$ as
$t\to+\infty$, where $\bar{u}_0=\frac{1}{|\Omega|}\int_\Omega u_0dx$.
Furthermore, the decay rate is exponential if $\frac{\xi\gamma}{\chi\alpha}>
\max\Big\{\frac{\beta}{\delta},\frac{\delta}{\beta}\Big\}$. This paper provides
the first results on the full ARKS system with unequal chemical diffusion rates
(i.e. $D_1\ne D_2$) in multi-dimensions.

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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: dg-ga