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Abstract
In this paper, we study the stability and convergence rate of
traveling wavefronts for a nonlocal population model in a periodic
habitat
\[
\left\{
\begin{array}{ll}
\displaystyle\frac{\partial u(t,x)}{\partial t}=D(x)\frac{\partial ^2u(t,x)}{%
\partial x^2}-d(x,u(t,x))+\int_R\Gamma (\tau ,x,y)b(y,u(t-\tau ,y))dy, & \\
u(\theta ,x)=\varphi (\theta ,x),\theta \in [-\tau ,0],&
\end{array}
\right.
\]
where $D(x), d(x,\cdot ), b(x,\cdot ), \Gamma (\tau ,x,y)$ are
L-periodic functions with respect to space $x$ (and $y$) for some
positive real constant $L $. Using the analysis of the principal
eigenvalue of a non-local linear operator, we show that all
noncritical wavefronts are globally exponentially stable, as long as
the initial perturbation is uniformly bounded in a weighted space.
This result can be generalized to n-dimensional case and three
applications of our main results are also presented.
Mathematics Subject Classification: Primary: 35K57, 34K20; Secondary: 92D25.
\begin{equation} \\ \end{equation}
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