تقرير
Weyl formulae for some singular metrics with application to acoustic modes in gas giants
| العنوان: | Weyl formulae for some singular metrics with application to acoustic modes in gas giants |
|---|---|
| المؤلفون: | de Verdìère, Yves Colin, Dietze, Charlotte, de Hoop, Maarten V., Trélat, Emmanuel |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Astrophysics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Astrophysics - Earth and Planetary Astrophysics, Mathematical Physics, Mathematics - Spectral Theory |
| الوصف: | This paper is motivated by recent works on inverse problems for acoustic wave propagation in the interior of gas giant planets. In such planets, the speed of sound is isotropic and tends to zero at the surface. Geometrically, this corresponds to a Riemannian manifold with boundary whose metric blows up near the boundary. Here, the spectral analysis of the corresponding Laplace-Beltrami operator is presented and the Weyl law is derived. The involved exponents depend on the Hausdorff dimension which, in the supercritical case, is larger than the topological dimension. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.19734 |
| رقم الأكسشن: | edsarx.2406.19734 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |