Dynamical boundary problem for Dirichlet-to-Neumann operator with critical Sobolev exponent and Hardy potential. (December 2021)

• Record Type: Journal Article
• Authors: Deng, Yanhua; Tan, Zhong; Xie, Minghong
• Is Part Of: Nonlinear analysis. Volume 62(2021)
• Publication Date: 2021-12
• Subjects: Dirichlet-to-Neumann operator -- Critical exponent -- Hardy potential -- Blowup -- Bubbling description; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103346
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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.