Asymptotic Approximation of Eigenelements of the Dirichlet Problem for the Laplacian in a Junction with Highly Oscillating Boundary

Youcef Amirat (1) , Gregory A. Chechkin (2, 3) , Rustem R. Gadyl'Shin (4)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 Department of Differential Equations
3 Narvik University College
4 Department of Mathematical Analysis

We study the asymptotic behavior of the eigenelements of the Dirichlet problem for the Laplacian in a bounded domain, a part of whose boundary, depending on a small parameter $\varepsilon$, is highly oscillating; the frequency of oscillations of the boundary is of order $\varepsilon$ and the amplitude is fixed. We construct and analyze second-order asymptotic approximations, as $\varepsilon \to 0$, of the eigenelements in the case of simple eigenvalues of the limit problem.

Domaines: Equations aux dérivées partielles [math.AP]

Youcef Amirat, Gregory A. Chechkin, Rustem R. Gadyl'Shin. Asymptotic Approximation of Eigenelements of the Dirichlet Problem for the Laplacian in a Junction with Highly Oscillating Boundary. 2008. ⟨hal-00282229⟩