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• W2893076715 abstract "In this article, we are concerned with the following eigenvalue problem of a linear second order elliptic operator: begin{equation} nonumber -DDelta phi -2alphanabla m(x)cdot nablaphi+V(x)phi=lambdaphi hbox{ in }Omega, end{equation} complemented by a general boundary condition including Dirichlet boundary condition and Robin boundary condition: $$ frac{partialphi}{partial n}+beta(x)phi=0 hbox{ on }partialOmega, $$ where $betain C(partialOmega)$ allows to be positive, sign-changing or negative, and $n(x)$ is the unit exterior normal to $partialOmega$ at $x$. The domain $Omegasubsetmathbb{R}^N$ is bounded and smooth, the constants $D>0$ and $alpha>0$ are, respectively, the diffusive and advection coefficients, and $min C^2(barOmega),,Vin C(barOmega)$ are given functions. We aim to investigate the asymptotic behavior of the principal eigenvalue of the above eigenvalue problem as the diffusive coefficient $Dto0$ or $Dtoinfty$. Our results, together with those of cite{CL2,DF,Fr} where the Nuemann boundary case (i.e., $beta=0$ on $partialOmega$) and Dirichlet boundary case were studied, reveal the important effect of advection and boundary conditions on the asymptotic behavior of the principal eigenvalue. We also apply our results to a reaction-diffusion-advection equation which is used to describe the evolution of a single species living in a heterogeneous stream environment and show some interesting behaviors of the species persistence and extinction caused by the buffer zone and small/large diffusion rate." @default.
• W2893076715 created "2018-10-05" @default.
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• W2893076715 date "2018-09-28" @default.
• W2893076715 modified "2023-09-25" @default.
• W2893076715 title "Asymptotic behavior of the principal eigenvalue of a linear second order elliptic operator with small/large diffusion coefficient and its application" @default.
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• W2893076715 hasPublicationYear "2018" @default.
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