Asymptotic analysis of a boundary-value problem in a thin cascade domain with a local joint

Abstract

A nonuniform Neumann boundary-value problem is considered for the Poisson equation in a thin domain ${\Omega }_{\epsilon }$ coinciding with two thin rectangles connected through a joint of diameter $\mathcal{O}(\epsilon )$. A rigorous procedure is developed to construct the complete asymptotic expansion for the solution as the small parameter $\epsilon \to 0.$ Energetic and uniform pointwise estimates for the difference between the solution of the starting problem $(\epsilon >0)$ and the solution of the corresponding limit problem $(\epsilon =0)$ are proved, from which the influence of the geometric irregularity of the joint is observed.

25 pages, 5 figures

References in corpus (1)

• Asymptotic Approximation for the Solution to a Semi-linear Parabolic Problem in a Thick Fractal Junction

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