Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains
This paper is concerned with an indefinite weight linear eigenvalueproblem in cylindrical domains. We investigate the minimization of the positiveprincipal eigenvalue under the constraint that the weight is bounded bya positive and a negative constant and the total weight is a fixed negativeconstant...
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| Format: | Article |
| Language: | English |
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AIMS Press
2008-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.315 |
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| _version_ | 1832590221381730304 |
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| author | Chiu-Yen Kao Yuan Lou Eiji Yanagida |
| author_facet | Chiu-Yen Kao Yuan Lou Eiji Yanagida |
| author_sort | Chiu-Yen Kao |
| collection | DOAJ |
| description | This paper is concerned with an indefinite weight linear eigenvalueproblem in cylindrical domains. We investigate the minimization of the positiveprincipal eigenvalue under the constraint that the weight is bounded bya positive and a negative constant and the total weight is a fixed negativeconstant. Biologically, this minimization problem is motivated by the questionof determining the optimal spatial arrangement of favorable and unfavorableregions for a species to survive. Both our analysis and numerical simulationsfor rectangular domains indicate that there exists a threshold value such thatif the total weight is below this threshold value, then the optimal favorableregion is a circular-type domain at one of the four corners, and a strip at theone end with shorter edge otherwise. |
| format | Article |
| id | doaj-art-d831171063c04fedbdeb7c03756a8d45 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2008-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-d831171063c04fedbdeb7c03756a8d452025-01-24T01:58:10ZengAIMS PressMathematical Biosciences and Engineering1551-00182008-02-015231533510.3934/mbe.2008.5.315Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domainsChiu-Yen Kao0Yuan Lou1Eiji Yanagida2Department of Mathematics, The Ohio State University, Columbus, OH 43210Department of Mathematics, The Ohio State University, Columbus, OH 43210Department of Mathematics, The Ohio State University, Columbus, OH 43210This paper is concerned with an indefinite weight linear eigenvalueproblem in cylindrical domains. We investigate the minimization of the positiveprincipal eigenvalue under the constraint that the weight is bounded bya positive and a negative constant and the total weight is a fixed negativeconstant. Biologically, this minimization problem is motivated by the questionof determining the optimal spatial arrangement of favorable and unfavorableregions for a species to survive. Both our analysis and numerical simulationsfor rectangular domains indicate that there exists a threshold value such thatif the total weight is below this threshold value, then the optimal favorableregion is a circular-type domain at one of the four corners, and a strip at theone end with shorter edge otherwise.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.315principal eigenvaluelocal minimizercylindrical domain. |
| spellingShingle | Chiu-Yen Kao Yuan Lou Eiji Yanagida Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains Mathematical Biosciences and Engineering principal eigenvalue local minimizer cylindrical domain. |
| title | Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains |
| title_full | Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains |
| title_fullStr | Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains |
| title_full_unstemmed | Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains |
| title_short | Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains |
| title_sort | principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains |
| topic | principal eigenvalue local minimizer cylindrical domain. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.315 |
| work_keys_str_mv | AT chiuyenkao principaleigenvalueforanellipticproblemwithindefiniteweightoncylindricaldomains AT yuanlou principaleigenvalueforanellipticproblemwithindefiniteweightoncylindricaldomains AT eijiyanagida principaleigenvalueforanellipticproblemwithindefiniteweightoncylindricaldomains |