The Buckling Operator: Inverse Boundary Value Problem
In this paper, we consider a zeroth-order perturbation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow>&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/2/268 |
| _version_ | 1797439055515877376 |
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| author | Yanjun Ma |
| author_facet | Yanjun Ma |
| author_sort | Yanjun Ma |
| collection | DOAJ |
| description | In this paper, we consider a zeroth-order perturbation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula> of the buckling operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mo>Δ</mo><mn>2</mn></msup><mo>−</mo><mi>κ</mi><mo>Δ</mo></mrow></semantics></math></inline-formula>, which can be uniquely determined by measuring the Dirichlet-to-Neumann data on the boundary. We extend the conclusion of the biharmonic operator to the buckling operator, but the Dirichlet-to-Neumann map given in this study is more meaningful and general. |
| first_indexed | 2024-03-09T11:47:17Z |
| format | Article |
| id | doaj.art-3775fd827f5f42848b19d9a99dde94f4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:47:17Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3775fd827f5f42848b19d9a99dde94f42023-11-30T23:19:48ZengMDPI AGMathematics2227-73902023-01-0111226810.3390/math11020268The Buckling Operator: Inverse Boundary Value ProblemYanjun Ma0School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, ChinaIn this paper, we consider a zeroth-order perturbation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula> of the buckling operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mo>Δ</mo><mn>2</mn></msup><mo>−</mo><mi>κ</mi><mo>Δ</mo></mrow></semantics></math></inline-formula>, which can be uniquely determined by measuring the Dirichlet-to-Neumann data on the boundary. We extend the conclusion of the biharmonic operator to the buckling operator, but the Dirichlet-to-Neumann map given in this study is more meaningful and general.https://www.mdpi.com/2227-7390/11/2/268Dirichlet-to-Neumann mapbuckling operatoruniqueness |
| spellingShingle | Yanjun Ma The Buckling Operator: Inverse Boundary Value Problem Mathematics Dirichlet-to-Neumann map buckling operator uniqueness |
| title | The Buckling Operator: Inverse Boundary Value Problem |
| title_full | The Buckling Operator: Inverse Boundary Value Problem |
| title_fullStr | The Buckling Operator: Inverse Boundary Value Problem |
| title_full_unstemmed | The Buckling Operator: Inverse Boundary Value Problem |
| title_short | The Buckling Operator: Inverse Boundary Value Problem |
| title_sort | buckling operator inverse boundary value problem |
| topic | Dirichlet-to-Neumann map buckling operator uniqueness |
| url | https://www.mdpi.com/2227-7390/11/2/268 |
| work_keys_str_mv | AT yanjunma thebucklingoperatorinverseboundaryvalueproblem AT yanjunma bucklingoperatorinverseboundaryvalueproblem |