主固有値の最小化と個体群ダイナミクス
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This article is concerned with an indefinite weight linear eigenvalue problem which is related with population dynamics. We investigate the minimization of the positive principal eigenvalue under the constraint that the weight is bounded by a positive and and a negative constant and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for a species to survive. 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. We also consider the case of rectangular domains both mathematically and numerically.
- 一般社団法人日本応用数理学会の論文
- 2013-06-25
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