arXiv subjects

Pablo Benavent-Ocejo

Publications and source records attributed to Pablo Benavent-Ocejo.

2 recordsLinked to original sources

arXiv2025

Asymptotics for the spectrum of the Laplacian in thin bars with varying cross sections

We consider spectral problems for Laplace operator in 3D rod structures with a small cross section of diameter $O(\varepsilon)$, $\varepsilon$ being a positive parameter. The boundary conditions are Dirichlet (Neumann, respectively) on the bases of this structure and Neumann on the lateral boundary. As $\varepsilon\to 0$, we show the convergence of the spectrum with conservation of the multiplicity towards that of a 1D spectral model with Dirichlet (Neumann, respectively) boundary conditions. This 1D model may arise in diffusion or vibrations models of nonhomogeneous media with different physical characteristics and it takes into account the geometry of the 3D domain. We deal with the low frequencies and the approach to eigenfunctions in the suitable Sobolev spaces is also outlined.

math.AP↗

arXiv2025

Longitudinal oscillations for eigenfunctions in rod like structures

We consider the spectrum of the Laplace operator on 3D rod structures, with a small cross section depending on a small parameter $\varepsilon$. The boundary conditions are of Dirichlet type on the basis of this structure and Neumann on the lateral boundary. We focus on the low frequencies. We study the asymptotic behavior of the eigenvalues and associated eigenfunctions, which are approached as $\varepsilon\to 0$ by those of a 1D model with Dirichlet boundary conditions, but which takes into account the geometry of the domain. Explicit and numerical computations enlighten the interest of this study, when the parameter becomes smaller. At the same time they show that in order to capture oscillations in the transverse direction we need to deal with the high frequencies. For prism like domains, we show the different asymptotic behavior of the spectrum depending on the boundary conditions.

math.AP↗