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October 2006 Minimization of the Principal Eigenvalue for an Elliptic Boundary Value Problem with Indefinite Weight, and Applications to Population Dynamics
Yuan Lou, Eiji Yanagida
Japan J. Indust. Appl. Math. 23(3): 275-292 (October 2006).

Abstract

This paper is concerned with an indefinite weight linear eigenvalue problem which is related with biological invasions of species. We investigate the minimization of the positive principal eigenvalue under the constraint that the weight is bounded by a positive and a negative constant and the total weight is a fixed negative constant. For an arbitrary domain, it is shown that every global minimizer must be of ``bang-bang'' type. When the domain is an interval, it is proved that there are exactly two global minimizers, for which the weight is positive at one end of the interval and is negative in the remainder. The biological implication is that a single favorable region at one end of the habitat provides the best opportunity for the species to survive, and also that the least fragmented habitat provides the best chance for the population to maintain its genetic variability.

Citation

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Yuan Lou. Eiji Yanagida. "Minimization of the Principal Eigenvalue for an Elliptic Boundary Value Problem with Indefinite Weight, and Applications to Population Dynamics." Japan J. Indust. Appl. Math. 23 (3) 275 - 292, October 2006.

Information

Published: October 2006
First available in Project Euclid: 11 December 2007

zbMATH: 1185.35059
MathSciNet: MR2281509

Rights: Copyright © 2006 The Japan Society for Industrial and Applied Mathematics

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Vol.23 • No. 3 • October 2006
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