Asymptotics of the solution of a Dirichlet spectral problem in a junction with highly oscillating boundary
Youcef Amirat, Gregory Aleksandrovich Chechkin, Rustem Rashitovich Gadyl'shin · Comptes Rendus Mécanique · 2008
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 ε , is highly oscillating; the frequency of oscillations of the boundary is of order ε and the amplitude is fixed. We present second-order asymptotic approximations, as ε → 0 , of the eigenelements in the case of simple eigenvalues of the limit problem.