1. Asymptotic analysis a perturbed Robin problem in a planar domain
- Author
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Musolino, Paolo, Dutko, Martin, and Mishuris, Gennady
- Subjects
Mathematics - Analysis of PDEs ,35J25, 31B10, 35B25, 35C20, 47H30 - Abstract
We consider a perforated domain $\Omega(\epsilon)$ of $\mathbb{R}^2$ with a small hole of size $\epsilon$ and we study the behavior of the solution of a mixed Neumann-Robin problem in $\Omega(\epsilon)$ as the size $\epsilon$ of the small hole tends to $0$. In addition to the geometric degeneracy of the problem, the $\epsilon$-dependent Robin condition may degenerate into a Neumann condition for $\epsilon=0$ and the Robin datum may diverge to infinity. Our goal is to analyze the asymptotic behavior of the solutions to the problem as $\epsilon$ tends to $0$ and understand how the boundary condition affects the behavior of the solutions when $\epsilon$ is close to $0$., Comment: arXiv admin note: text overlap with arXiv:2208.02695
- Published
- 2023