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Principal eigenvalue and eigenfunctions of an elliptic operator with large advection and its application to a competition model. (English) Zbl 1153.35056

This article is devoted to studying the asymptotic behavior of the principal eigenvalue and eigenfunction for an elliptic operator. The asymptotic behavior, as the coefficient of the advection term approaches infinity, of the principal eigenvalue and the limiting profiles of the corresponding eigenfunctions of an elliptic operator are found. Authors investigate a Lotka-Volterra reaction diffusion advection model for two competing species in a heterogeneous environment as an application.

MSC:

35P15 Estimates of eigenvalues in context of PDEs
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
92D25 Population dynamics (general)
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