We study the Laplacian equation with dynamical boundary condition involving Dirichlet-to-Neumann operator, critical growth, and Hardy potential. We first prove the existence and decay estimates of global solutions and finite time blowup of local solutions under certain assumptions. Then we focus on the asymptotic behavior of global solutions approaching a stationary solution in the long time series. Furthermore, we give a precise bubbling description by the concentration-compactness principle.

中文翻译：

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具有临界Sobolev指数和Hardy势的Dirichlet-to-Neumann算子的动力学边界问题

我们研究了具有动态边界条件的Laplacian方程，其中涉及Dirichlet-to-Neumann算子，临界增长和Hardy势。我们首先证明在某些假设下全局解的存在和衰减估计以及局部解的有限时间爆炸。然后，我们关注长时间序列中趋近平稳解的整体解的渐近行为。此外，我们通过浓度紧凑原理给出了精确的起泡描述。