On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of the Robin Problem with Large Parameter
We consider the eigenvalue problem with Robin boundary condition ∆u + λu = 0 in Ω, ∂u/∂ν + αu = 0 on ∂Ω, where Ω ⊂ Rn , n ≥ 2 is a bounded domain with a smooth boundary, ν is the outward unit normal, α is a real parameter. We obtain two terms of the asymptotic expansion of simple eigenvalues of this...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2017-01-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/872 |
| _version_ | 1819279917118914560 |
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| author | Alexey V. Filinovskiy |
| author_facet | Alexey V. Filinovskiy |
| author_sort | Alexey V. Filinovskiy |
| collection | DOAJ |
| description | We consider the eigenvalue problem with Robin boundary condition ∆u + λu = 0 in Ω, ∂u/∂ν + αu = 0 on ∂Ω, where Ω ⊂ Rn , n ≥ 2 is a bounded domain with a smooth boundary, ν is the outward unit normal, α is a real parameter. We obtain two terms of the asymptotic expansion of simple eigenvalues of this problem for α → +∞. We also prove an estimate to the difference between Robin and Dirichlet eigenfunctions. |
| first_indexed | 2024-12-24T00:35:31Z |
| format | Article |
| id | doaj.art-ccefc8d3b5ef4acf865091614396f390 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-24T00:35:31Z |
| publishDate | 2017-01-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-ccefc8d3b5ef4acf865091614396f3902022-12-21T17:24:05ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102017-01-0122110.3846/13926292.2017.1263244On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of the Robin Problem with Large ParameterAlexey V. Filinovskiy0Department of High Mathematics, Faculty of Fundamental Sciences, Bauman Moscow State Technical University, 2nd Baumanskaya st. 5, 105005 Moscow, Russia; Department of Differential Equations, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory 1, 119991 Moscow, RussiaWe consider the eigenvalue problem with Robin boundary condition ∆u + λu = 0 in Ω, ∂u/∂ν + αu = 0 on ∂Ω, where Ω ⊂ Rn , n ≥ 2 is a bounded domain with a smooth boundary, ν is the outward unit normal, α is a real parameter. We obtain two terms of the asymptotic expansion of simple eigenvalues of this problem for α → +∞. We also prove an estimate to the difference between Robin and Dirichlet eigenfunctions.https://journals.vgtu.lt/index.php/MMA/article/view/872Laplace operatorRobin boundary conditioneigenvalues and eigenfunctionslarge parameterasymptotic behavior |
| spellingShingle | Alexey V. Filinovskiy On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of the Robin Problem with Large Parameter Mathematical Modelling and Analysis Laplace operator Robin boundary condition eigenvalues and eigenfunctions large parameter asymptotic behavior |
| title | On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of the Robin Problem with Large Parameter |
| title_full | On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of the Robin Problem with Large Parameter |
| title_fullStr | On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of the Robin Problem with Large Parameter |
| title_full_unstemmed | On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of the Robin Problem with Large Parameter |
| title_short | On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of the Robin Problem with Large Parameter |
| title_sort | on the asymptotic behavior of eigenvalues and eigenfunctions of the robin problem with large parameter |
| topic | Laplace operator Robin boundary condition eigenvalues and eigenfunctions large parameter asymptotic behavior |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/872 |
| work_keys_str_mv | AT alexeyvfilinovskiy ontheasymptoticbehaviorofeigenvaluesandeigenfunctionsoftherobinproblemwithlargeparameter |