Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pulsating Fronts for a Bistable Lotka-Volterra Competition System with
  Advection in a Periodic Habitat   This paper is concerned with the following Lotka-Volterra competition system
with advection in a periodic habitat \begin{equation*} \begin{cases}
\frac{\partial u_1}{\partial t} =d_1(x)\frac{\partial^2 u_1}{\partial
x^2}-a_1(x)\frac{\partial u_1}{\partial
x}+u_1\left(b_1(x)-a_{11}(x)u_1-a_{12}(x)u_2\right),\\ \frac{\partial
u_2}{\partial t} =d_2(x)\frac{\partial^2 u_2}{\partial
x^2}-a_2(x)\frac{\partial u_2}{\partial
x}+u_2\left(b_2(x)-a_{21}(x)u_1-a_{22}(x)u_2\right), \end{cases} t>0,~x\in\Bbb
R, \end{equation*} where $d_i(\cdot)$, $a_i(\cdot)$, $b_i(\cdot)$,
$a_{ij}(\cdot)$ $(i,j=1,2)$ are $L$-periodic functions in $C^\nu(\Bbb{R})$ with
some $\nu\in(0,1)$. Under certain assumptions, the system admits two periodic
locally stable steady states $(u_1^*(x),0)$ and $(0,u_2^*(x))$. In this work,
we first establish the existence of the pulsating front
$U(x,x+ct)=(U_1(x,x+ct),U_2(x,x+ct))$ connecting two periodic solutions
$(0,u_2^*(x))$ and $(u_1^*(x),0)$ at infinities. By using a dynamical method,
we confirm further that the pulsating front is asymptotically stable for
front-like initial values. As a consequence of the global asymptotically
stability, we finally show that the pulsating front is unique up to
translation.

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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex