Waveguide with non-periodically alternating Dirichlet and Robin conditions: homogenization and asymptotics
We consider a magnetic Schrödinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary conditions. Assuming that the homogenized boundary condition is the Dirichlet or the Robin one, we establish the uniform resolvent convergence in vario...
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| Published in | Zeitschrift für angewandte Mathematik und Physik Vol. 64; no. 3; pp. 439 - 472 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Basel
SP Birkhäuser Verlag Basel
01.06.2013
Springer Verlag |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0044-2275 1420-9039 |
| DOI | 10.1007/s00033-012-0264-2 |
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| Abstract | We consider a magnetic Schrödinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary conditions. Assuming that the homogenized boundary condition is the Dirichlet or the Robin one, we establish the uniform resolvent convergence in various operator norms and we prove the estimates for the rates of convergence. It is shown that these estimates can be improved by using special boundary correctors. In the case of periodic alternation, pure Laplacian, and the homogenized Robin boundary condition, we construct two-terms asymptotics for the first band functions, as well as the complete asymptotics expansion (up to an exponentially small term) for the bottom of the band spectrum. |
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| AbstractList | We consider a magnetic Schrodinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary conditions. Assuming that the homogenized boundary condition is the Dirichlet or the Robin one, we establish the uniform resolvent convergence in various operator norms and we prove the estimates for the rates of convergence. It is shown that these estimates can be improved by using special boundary correctors. In the case of periodic alternation, pure Laplacian, and the homogenized Robin boundary condition, we construct two-terms asymptotics for the first band functions, as well as the complete asymptotics expansion (up to an exponentially small term) for the bottom of the band spectrum. We consider a magnetic Schrödinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary conditions. Assuming that the homogenized boundary condition is the Dirichlet or the Robin one, we establish the uniform resolvent convergence in various operator norms and we prove the estimates for the rates of convergence. It is shown that these estimates can be improved by using special boundary correctors. In the case of periodic alternation, pure Laplacian, and the homogenized Robin boundary condition, we construct two-terms asymptotics for the first band functions, as well as the complete asymptotics expansion (up to an exponentially small term) for the bottom of the band spectrum. Mathematics Subject Classification(2010). 35B27 · 35J15 · 35P05. We consider a magnetic Schrödinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary conditions. Assuming that the homogenized boundary condition is the Dirichlet or the Robin one, we establish the uniform resolvent convergence in various operator norms and we prove the estimates for the rates of convergence. It is shown that these estimates can be improved by using special boundary correctors. In the case of periodic alternation, pure Laplacian, and the homogenized Robin boundary condition, we construct two-terms asymptotics for the first band functions, as well as the complete asymptotics expansion (up to an exponentially small term) for the bottom of the band spectrum. |
| Author | Bunoiu, Renata Cardone, Giuseppe Borisov, Denis |
| Author_xml | – sequence: 1 givenname: Denis surname: Borisov fullname: Borisov, Denis email: borisovdi@yandex.ru organization: Institute of Mathematics of Ufa Scientific Center of RAS, Bashkir State Pedagogical University – sequence: 2 givenname: Renata surname: Bunoiu fullname: Bunoiu, Renata organization: LMAM, UMR 7122, Université de Lorraine et CNRS – sequence: 3 givenname: Giuseppe surname: Cardone fullname: Cardone, Giuseppe organization: Department of Engineering, Giuseppe Cardone University of Sannio |
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| Keywords | 35B27 Uniform resolvent convergence Band spectrum 35P05 Alternating boundary conditions 35J15 Asymptotics Waveguide |
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| Snippet | We consider a magnetic Schrödinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary... We consider a magnetic Schrodinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary... |
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| SubjectTerms | Asymptotic properties Engineering Mathematical Methods in Physics Mathematics Theoretical and Applied Mechanics |
| Title | Waveguide with non-periodically alternating Dirichlet and Robin conditions: homogenization and asymptotics |
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