Dynamical boundary problem for Dirichlet-to-Neumann operator with critical Sobolev exponent and Hardy potential

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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.