Asymptotic expansion for the solution to a boundary-value problem in a thin cascade domain with a local joint (Q2814644)

In this paper, the authors consider a uniform Neumann boundary-value problem for the Poisson equation in a thin domain \(\Omega_{\varepsilon}\) coinciding with two thin rectangles connected trough of diameter \(O(\varepsilon)\). They construct the complete asymptotic expansion of the solution to this problem. Furthermore, they give the proof energetic and pointwise uniform estimates for the difference between the solution of the problem at \(\varepsilon > 0\) and the one of the problem at \(\varepsilon = 0\). In addition, these boundary layer solutions have polynomial grow at infinity. Finally, they obtain the impact of the geometric irregularity and material characteristics of the joint on some proprieties of the whole structure.