论文标题
刻度的刻度相互作用，用于奇异的扰动退化非线性robin问题
Interaction of scales for a singularly perturbed degenerating nonlinear Robin problem
论文作者
论文摘要
我们研究了在$ \ Mathbb {r}^n $，$ n \ geq 3 $中，在$ \ mathbb {r}^n $中的laplace方程的解决方案的渐近行为，其在小孔的边界上具有（非线性的）robin边界条件。我们希望考虑在三个方面退化的问题：在极限情况下，罗宾边界条件可能退化为诺伊曼边界条件，罗宾基准可能趋于无穷大，并且小孔的尺寸$ε$，我们认为罗宾条件崩溃至$ 0 $。我们研究了这三个奇异性如何相互作用并影响渐近行为，因为$ε$倾向于$ 0 $，并且我们代表解决方案及其能量积分，它在真实的分析图和已知功能的奇异扰动参数方面。
We study the asymptotic behavior of the solutions of a boundary value problem for the Laplace equation in a perforated domain in $\mathbb{R}^n$, $n\geq 3$, with a (nonlinear) Robin boundary condition on the boundary of the small hole. The problem we wish to consider degenerates under three aspects: in the limit case the Robin boundary condition may degenerate into a Neumann boundary condition, the Robin datum may tend to infinity, and the size $ε$ of the small hole where we consider the Robin condition collapses to $0$. We study how these three singularities interact and affect the asymptotic behavior as $ε$ tends to $0$, and we represent the solution and its energy integral in terms of real analytic maps and known functions of the singular perturbation parameters.
