Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains.
Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains.
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DOI：
10.3934/mbe.2008.5.315
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发表时间：
2008-03
期刊：
影响因子：
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通讯作者：
C. Kao;Y. Lou;E. Yanagida
中科院分区：
文献类型：
--
作者：
C. Kao;Y. Lou;E. Yanagida
本文研究柱域上的不定权线性特征值问题。本文研究了在权值为一个正、一个负常数且总权值为一个固定的负常数的约束下，正主特征值的极小化问题。生物学上，这个最小化问题的动机是确定一个物种生存的有利和不利区域的最佳空间安排的问题。我们的分析和数值模拟矩形域表明，存在一个阈值，使得如果总重量是低于这个阈值，那么最佳的有利区域是一个圆形的域的四个角之一，和一个带的一端与较短的边缘，否则。
This paper is concerned with an indefinite weight linear eigenvalue problem in cylindrical domains. 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. 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. Both our analysis and numerical simulations for rectangular domains indicate that there exists a threshold value such that if the total weight is below this threshold value, then the optimal favorable region is a circular-type domain at one of the four corners, and a strip at the one end with shorter edge otherwise.