التفاصيل البيبلوغرافية
| العنوان: |
Variational approach to scattering of plane elastic waves by diffraction gratings |
| المؤلفون: |
Guanghui Hu, Johannes Elschner |
| بيانات النشر: |
Weierstrass Institute, 2009. |
| سنة النشر: |
2009 |
| مصطلحات موضوعية: |
variational formulation, Plane (geometry), Sesquilinear form, Scattering, General Mathematics, Operator (physics), Elastic waves, Mathematical analysis, General Engineering, diffraction gratings, 35J55, Lipschitz continuity, 74B05, Navier equation, 74J20, Sobolev space, Quasiperiodic function, 35Q72, Uniqueness, Mathematics |
| الوصف: |
The scattering of a time-harmonic plane elastic wave by a two-dimensional periodic structure is studied. The grating profile is given by a Lipschitz curve on which the displacement vanishes. Using a variational formulation in a bounded periodic cell involving a nonlocal boundary operator, existence of solutions in quasiperiodic Sobolev spaces is investigated by establishing the Fredholmness of the operator generated by the corresponding sesquilinear form. Moreover, by a Rellich identity, uniqueness is proved under the assumption that the grating profile is given by a Lipschitz graph. The direct scattering problem for transmission gratings is also investigated. In this case, uniqueness is proved except for a discrete set of frequencies. Copyright © 2010 John Wiley & Sons, Ltd. |
| DOI: |
10.20347/wias.preprint.1466 |
| الوصول الحر: |
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::13c50d357c72c8269ffee5d01f941205Test |
| حقوق: |
CLOSED |
| رقم الانضمام: |
edsair.doi.dedup.....13c50d357c72c8269ffee5d01f941205 |
| قاعدة البيانات: |
OpenAIRE |
