%0 Journal Article %1 lou2006minimization %A Lou, Yuan %A Yanagida, Eiji %D 2006 %J Japan J. Indust. Appl. Math. %K eigenvalue_problem fishers_diffusion probability_of_survival spatial_structure %N 3 %P 275--292 %T Minimization of the principal eigenvalue for an elliptic boundary value problem with indefinite weight, and applications to population dynamics %U http://projecteuclid.org/euclid.jjiam/1197390801 %V 23 %X 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.

@article{lou2006minimization, 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.}, added-at = {2013-03-13T12:56:20.000+0100}, author = {Lou, Yuan and Yanagida, Eiji}, biburl = {https://www.bibsonomy.org/bibtex/206eb0bf0bb9f8cdc94eb12b1c4f58525/peter.ralph}, fjournal = {Japan Journal of Industrial and Applied Mathematics}, interhash = {e81e41ea5d3616b1429355ebf3a70760}, intrahash = {06eb0bf0bb9f8cdc94eb12b1c4f58525}, issn = {0916-7005}, journal = {Japan J. Indust. Appl. Math.}, keywords = {eigenvalue_problem fishers_diffusion probability_of_survival spatial_structure}, mrclass = {35J25 (35K25 35P15 47J30 92D25)}, mrnumber = {2281509 (2008i:35044)}, number = 3, pages = {275--292}, timestamp = {2014-12-17T22:50:59.000+0100}, title = {Minimization of the principal eigenvalue for an elliptic boundary value problem with indefinite weight, and applications to population dynamics}, url = {http://projecteuclid.org/euclid.jjiam/1197390801}, volume = 23, year = 2006 }