1. ASYMPTOTIC ANALYSIS OF PERTURBED ROBIN PROBLEMS IN A PLANAR DOMAIN.
- Author
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MUSOLINO, PAOLO, DUTKO, MARTIN, and MISHURIS, GENNADY
- Abstract
We consider a perforated domain Ω(ε) of R² with a small hole of size ε and we study the behavior of the solution of a mixed Neumann-Robin problem in Ω(ε) as the size ε of the small hole tends to 0. In addition to the geometric degeneracy of the problem, the nonlinear ε-dependent Robin condition may degenerate into a Neumann condition for ε = 0 and the Robin datum may diverge to infinity. Our goal is to analyze the asymptotic behavior of the solutions to the problem as ε tends to 0 and to understand how the boundary condition affects the behavior of the solutions when ε is close to 0. The present paper extends to the planar case the results of [36] dealing with the case of dimension n ≥ 3. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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